Topic 2: Mechanics

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

The electron is replaced by a proton which is also released from rest at X. Compare, without calculation, the motion of the electron with the motion of the proton after release. You may assume that no frictional forces act on the electron or the proton.

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

The diagram shows the forces acting on a block resting on an inclined plane. The angle θ is adjusted until the block is just at the point of sliding. R is the normal reaction, W the weight of the block and F the maximum frictional force.

What is the maximum coefficient of static friction between the block and the plane?

A. sin θ

B. cos θ

C. tan θ

D. $\frac{1}{\text{tan}\theta }$

The diagram shows the forces acting on a block resting on an inclined plane. The angle θ is adjusted until the block is just at the point of sliding. R is the normal reaction, W the weight of the block and F the maximum frictional force.

What is the maximum coefficient of static friction between the block and the plane?

A. sin θ

B. cos θ

C. tan θ

D. $\frac{1}{\text{tan}\theta }$

A system that consists of a single spring stores a total elastic potential energy E_p when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.

What is the total elastic potential energy stored in the changed system?

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

A system that consists of a single spring stores a total elastic potential energy E_p when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.

What is the total elastic potential energy stored in the changed system?

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.

When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s^–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s^–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 m s^–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.

between B and C.

between B and C.

between B and C.

An object falls from rest from a height h close to the surface of the Moon. The Moon has no atmosphere.

When the object has fallen to height $\frac{h}{4}$ above the surface, what is

                                      $\frac{\text{kinetic energy of the object at }\frac{h}{4}}{\text{gravitational potential energy of the object at }h}$?

A.     $\frac{3}{4}$

B.     $\frac{4}{3}$

C.     $\frac{9}{16}$

D.     $\frac{16}{9}$

An object falls from rest from a height h close to the surface of the Moon. The Moon has no atmosphere.

When the object has fallen to height $\frac{h}{4}$ above the surface, what is

                                      $\frac{\text{kinetic energy of the object at }\frac{h}{4}}{\text{gravitational potential energy of the object at }h}$?

A.     $\frac{3}{4}$

B.     $\frac{4}{3}$

C.     $\frac{9}{16}$

D.     $\frac{16}{9}$

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Show that the acceleration of the sledge is about –2 m s^–2.

At position B the rope starts to extend. Calculate the speed of the block at position B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Determine the magnitude of the average resultant force acting on the block between B and C.

Show that the acceleration of the sledge is about –2 m s^–2.

Show that the acceleration of the sledge is about –2 m s^–2.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

Determine the magnitude of the average resultant force acting on the block between B and C.

Determine the magnitude of the average resultant force acting on the block between B and C.

An object is moving in a straight line. A force F and a resistive force f act on the object along the straight line.

Both forces act for a time t.

What is the rate of change of momentum with time of the object during time t ?

A.     F + f 

B.     F – f

C.     (F + f )t

D.     (F – f )t 

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

Calculate the distance along the slope at which the sledge stops moving. Assume that the coefficient of dynamic friction is constant.

An object is moving in a straight line. A force F and a resistive force f act on the object along the straight line.

Both forces act for a time t.

What is the rate of change of momentum with time of the object during time t ?

A.     F + f 

B.     F – f

C.     (F + f )t

D.     (F – f )t 

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

between A and B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

between A and B.

between A and B.

At position B the rope starts to extend. Calculate the speed of the block at position B.

Determine the magnitude of the average resultant force acting on the block between B and C.

between B and C.

between B and C.

between B and C.

Determine the magnitude of the average resultant force acting on the block between B and C.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

Determine the magnitude of the average resultant force acting on the block between B and C.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Describe the effect of F on the linear speed of the wheel.

Describe the effect of F on the linear speed of the wheel.

Describe the effect of F on the linear speed of the wheel.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

Calculate the magnitude of the average force exerted by the rope on the block between B and C.

between A and B.

between A and B.

between A and B.

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

A weight W is tied to a trolley of mass M by a light string passing over a frictionless pulley. The trolley has an acceleration a on a frictionless table. The acceleration due to gravity is g.

What is W ?

A.    $\frac{Mag}{(g-a)}$

B.    $\frac{Mag}{(g+a)}$

C.    $\frac{Ma}{(g-a)}$

D.     $\frac{Ma}{(g+a)}$

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

A weight W is tied to a trolley of mass M by a light string passing over a frictionless pulley. The trolley has an acceleration a on a frictionless table. The acceleration due to gravity is g.

What is W ?

A.    $\frac{Mag}{(g-a)}$

B.    $\frac{Mag}{(g+a)}$

C.    $\frac{Ma}{(g-a)}$

D.     $\frac{Ma}{(g+a)}$

An electron is emitted from the photoelectric surface with kinetic energy 2.1 eV. Calculate the speed of the electron at the collecting plate.

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

A ball of mass m collides with a vertical wall with an initial horizontal speed u and rebounds with a horizontal speed v. The graph shows the variation of the speed of the ball with time.

What is the magnitude of the mean net force on the ball during the collision?

A.     $\frac{m(u-v)}{(t_2+t_1)}$

B.     $\frac{m(u-v)}{(t_2-t_1)}$

C.     $\frac{m(u+v)}{(t_2+t_1)}$

D.     $\frac{m(u+v)}{(t_2-t_1)}$

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

A ball of mass m collides with a vertical wall with an initial horizontal speed u and rebounds with a horizontal speed v. The graph shows the variation of the speed of the ball with time.

What is the magnitude of the mean net force on the ball during the collision?

A.     $\frac{m(u-v)}{(t_2+t_1)}$

B.     $\frac{m(u-v)}{(t_2-t_1)}$

C.     $\frac{m(u+v)}{(t_2+t_1)}$

D.     $\frac{m(u+v)}{(t_2-t_1)}$

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

Show that the magnitude of the net force F on the ball is given by the following equation.

                                          $$F=\frac{mg}{\tan \theta }$$

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

The radius of the bowl is 8.0 m and θ = 22°. Determine the speed of the ball.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

Outline whether this ball can move on a horizontal circular path of radius equal to the radius of the bowl.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A second identical ball is placed at the bottom of the bowl and the first ball is displaced so that its height from the horizontal is equal to 8.0 m.

The first ball is released and eventually strikes the second ball. The two balls remain in contact. Determine, in m, the maximum height reached by the two balls.

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

Determine the magnitude of the average decelerating force that the ground exerts on the egg.

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Determine the initial acceleration of the spacecraft.

Show that the kinetic energy of the egg just before impact is about 0.6 J.

Determine the initial acceleration of the spacecraft.

Show that the kinetic energy of the egg just before impact is about 0.6 J.

Show that the kinetic energy of the egg just before impact is about 0.6 J.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

Determine the initial acceleration of the spacecraft.

Estimate the maximum speed of the spacecraft.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

The egg comes to rest in a time of 55 ms. Determine the magnitude of the average decelerating force that the ground exerts on the egg.

A compressed spring is used to launch an object along a horizontal frictionless surface. When the spring is compressed through a distance $x$ and released, the object leaves the spring at speed $v$. What is the distance through which the spring must be compressed for the object to leave the spring at $\frac{v}{2}$?

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

A compressed spring is used to launch an object along a horizontal frictionless surface. When the spring is compressed through a distance $x$ and released, the object leaves the spring at speed $v$. What is the distance through which the spring must be compressed for the object to leave the spring at $\frac{v}{2}$?

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

Estimate the maximum speed of the spacecraft.

A ball of mass m collides with a wall and bounces back in a straight line. The ball loses 75 % of the initial energy during the collision. The speed before the collision is v.

What is the magnitude of the impulse on the ball by the wall?

A.   $\left(1-\frac{\sqrt{3}}{2}\right)mv$

B.   $\frac{1}{2}mv$

C.   $\frac{5}{4}mv$

D.   $\frac{3}{2}mv$

Estimate the maximum speed of the spacecraft.

A ball of mass m collides with a wall and bounces back in a straight line. The ball loses 75 % of the initial energy during the collision. The speed before the collision is v.

What is the magnitude of the impulse on the ball by the wall?

A.   $\left(1-\frac{\sqrt{3}}{2}\right)mv$

B.   $\frac{1}{2}mv$

C.   $\frac{5}{4}mv$

D.   $\frac{3}{2}mv$

Determine the initial acceleration of the spacecraft.

Determine the initial acceleration of the spacecraft.

Determine the initial acceleration of the spacecraft.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

(i) Estimate the maximum speed of the spacecraft.

(ii) Outline why the answer to (i) is an estimate.

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

Calculate the average force exerted by the racquet on the ball.

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

Calculate the average force exerted by the racquet on the ball.

Calculate the average force exerted by the racquet on the ball.

Friction and air resistance act on the bicycle and the girl when they move. Assume that all the energy is transferred from the battery to the electric motor. Determine the total average resistive force that acts on the bicycle and the girl.

The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).

Calculate the maximum speed of the bicycle and the girl up the slope.

Calculate the average power delivered to the ball during the impact.

The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).

Calculate the maximum speed of the bicycle and the girl up the slope.

Calculate the average power delivered to the ball during the impact.

Calculate the average power delivered to the ball during the impact.

Calculate the time it takes the tennis ball to reach the net.

The battery continues to give an output power of 240 W. Assume that the resistive forces are the same as in (a)(iii).

Calculate the maximum speed of the bicycle and the girl up the slope.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

A ball is thrown upwards at an angle to the horizontal. Air resistance is negligible. Which statement about the motion of the ball is correct?

A. The acceleration of the ball changes during its flight.

B. The velocity of the ball changes during its flight.

C. The acceleration of the ball is zero at the highest point.

D. The velocity of the ball is zero at the highest point.

An object of mass m is sliding down a ramp at constant speed. During the motion it travels a distance $x$ along the ramp and falls through a vertical distance h. The coefficient of dynamic friction between the ramp and the object is μ. What is the total energy transferred into thermal energy when the object travels distance $x$?

A. mgh

B. mgx

C. μmgh

D. μmgx

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

An object of mass m is sliding down a ramp at constant speed. During the motion it travels a distance $x$ along the ramp and falls through a vertical distance h. The coefficient of dynamic friction between the ramp and the object is μ. What is the total energy transferred into thermal energy when the object travels distance $x$?

A. mgh

B. mgx

C. μmgh

D. μmgx

Two blocks of masses m and 2m are travelling directly towards each other. Both are moving at the same constant speed v. The blocks collide and stick together.

What is the total momentum of the system before and after the collision?

Two blocks of masses m and 2m are travelling directly towards each other. Both are moving at the same constant speed v. The blocks collide and stick together.

What is the total momentum of the system before and after the collision?

The graph shows the variation with time of the resultant net force acting on an object. The object has a mass of 1kg and is initially at rest.

What is the velocity of the object at a time of 200 ms?

A. 8 m s^–1

B. 16 m s^–1

C. 8 km s^–1

D. 16 km s^–1

The graph shows the variation with time of the resultant net force acting on an object. The object has a mass of 1kg and is initially at rest.

What is the velocity of the object at a time of 200 ms?

A. 8 m s^–1

B. 16 m s^–1

C. 8 km s^–1

D. 16 km s^–1

A block is on the surface of a horizontal rotating disk. The block is at rest relative to the disk. The disk is rotating at constant angular velocity.

What is the correct arrow to represent the direction of the frictional force acting on the block at the instant shown?

A block is on the surface of a horizontal rotating disk. The block is at rest relative to the disk. The disk is rotating at constant angular velocity.

What is the correct arrow to represent the direction of the frictional force acting on the block at the instant shown?

An object has a weight of 6.10 × 10² N. What is the change in gravitational potential energy of the object when it moves through 8.0 m vertically?

A. 5 kJ

B. 4.9 kJ

C. 4.88 kJ

D. 4.880 kJ

A sports car is accelerated from 0 to 100 km per hour in 3 s. What is the acceleration of the car?

A. 0.1 g

B. 0.3 g

C. 0.9 g

D. 3 g

An object has a weight of 6.10 × 10² N. What is the change in gravitational potential energy of the object when it moves through 8.0 m vertically?

A. 5 kJ

B. 4.9 kJ

C. 4.88 kJ

D. 4.880 kJ

A sports car is accelerated from 0 to 100 km per hour in 3 s. What is the acceleration of the car?

A. 0.1 g

B. 0.3 g

C. 0.9 g

D. 3 g

A girl throws an object horizontally at time t = 0. Air resistance can be ignored. At t = 0.50 s the object travels horizontally a distance $x$ in metres while it falls vertically through a distance $y$ in metres.

What is the initial velocity of the object and the vertical distance fallen at t = 1.0 s?

A girl throws an object horizontally at time t = 0. Air resistance can be ignored. At t = 0.50 s the object travels horizontally a distance $x$ in metres while it falls vertically through a distance $y$ in metres.

What is the initial velocity of the object and the vertical distance fallen at t = 1.0 s?

Calculate the average force exerted by the racquet on the ball.

Calculate the average force exerted by the racquet on the ball.

Calculate the average force exerted by the racquet on the ball.

Outline why this force does no work on the Moon.

Calculate the average power delivered to the ball during the impact.

Calculate the average power delivered to the ball during the impact.

Calculate the average power delivered to the ball during the impact.

Outline why this force does no work on the Moon.

Outline why this force does no work on the Moon.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

Calculate the time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

Outline why this force does no work on Phobos.

Show that the tennis ball passes over the net.

Show that the tennis ball passes over the net.

Determine the speed of the tennis ball as it strikes the ground.

Outline why this force does no work on Phobos.

Determine the speed of the tennis ball as it strikes the ground.

Determine the speed of the tennis ball as it strikes the ground.

Outline why this force does no work on Phobos.

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.

Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

The speed of the proton is 2.16 × 10⁶ m s^-1 and the magnetic field strength is 0.042 T. For this proton, determine, in m, the radius of the circular path. Give your answer to an appropriate number of significant figures.

Sketch, on the axes, a graph to show the variation of gravitational potential energy with time for the bob and the object after the collision. The data from the graph used in (a) is shown as a dashed line for reference.

Calculate the speed of the ball as it leaves the racket.

An object hangs from a light string and moves in a horizontal circle of radius r.

The string makes an angle θ with the vertical. The angular speed of the object is ω. What is tan θ?

A. $\frac{{\omega }^{2}r}{g}$

B. $\frac{g}{{\omega }^{2}r}$

C. $\frac{\omega r^2}{g}$

D. $\frac{g}{\omega r^2}$

Calculate the speed of the ball as it leaves the racket.

An object hangs from a light string and moves in a horizontal circle of radius r.

The string makes an angle θ with the vertical. The angular speed of the object is ω. What is tan θ?

A. $\frac{{\omega }^{2}r}{g}$

B. $\frac{g}{{\omega }^{2}r}$

C. $\frac{\omega r^2}{g}$

D. $\frac{g}{\omega r^2}$

An object of mass m makes n revolutions per second around a circle of radius r at a constant speed. What is the kinetic energy of the object?

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

D. $4{\pi }^{2}m{n}^2{r}^2$

Calculate the speed of the ball as it leaves the racket.

Show that the average force exerted on the ball by the racket is about 50 N.

A climber of mass m slides down a vertical rope with an average acceleration a. What is the average frictional force exerted by the rope on the climber?

A. mg

B. m(g + a)

C. m(g – a)

D. ma

Show that the average force exerted on the ball by the racket is about 50 N.

A climber of mass m slides down a vertical rope with an average acceleration a. What is the average frictional force exerted by the rope on the climber?

A. mg

B. m(g + a)

C. m(g – a)

D. ma

An object of mass m makes n revolutions per second around a circle of radius r at a constant speed. What is the kinetic energy of the object?

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

D. $4{\pi }^{2}m{n}^2{r}^2$

Show that the average force exerted on the ball by the racket is about 50 N.

Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.

Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.

Determine, with reference to the work done by the average force, the horizontal distance travelled by the ball while it was in contact with the racket.

The tension in a horizontal spring is directly proportional to the extension of the spring. The energy stored in the spring at extension $x$ is $E$. What is the work done by the spring when its extension changes from $x$ to $\frac{x}{4}$?

A. $\frac{E}{16}$

B. $\frac{E}{4}$

C. $\frac{3E}{4}$

D. $\frac{15E}{16}$

The tension in a horizontal spring is directly proportional to the extension of the spring. The energy stored in the spring at extension $x$ is $E$. What is the work done by the spring when its extension changes from $x$ to $\frac{x}{4}$?

A. $\frac{E}{16}$

B. $\frac{E}{4}$

C. $\frac{3E}{4}$

D. $\frac{15E}{16}$

Comment on the magnitude of the force in (b)(ii).

An object of mass $1 \mathrm{kg}$ is thrown downwards from a height of $20 \mathrm{m}$. The initial speed of the object is $6 \mathrm{m} {\mathrm{s}}^{-1}$.
The object hits the ground at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$. What is the best estimate of the energy transferred from the object to the air as it falls?

A.  $6 \mathrm{J}$

B.  $18 \mathrm{J}$

C.  $182 \mathrm{J}$

D.  $200 \mathrm{J}$

An object of mass $2m$ moving at velocity $3v$ collides with a stationary object of mass $4m$. The objects stick together after the collision. What is the final speed and the change in total kinetic energy immediately after the collision?

Comment on the magnitude of the force in (b)(ii).

Comment on the magnitude of the force in (b)(ii).

Show that the radius of the path is about 6 cm.

An object of mass $2m$ moving at velocity $3v$ collides with a stationary object of mass $4m$. The objects stick together after the collision. What is the final speed and the change in total kinetic energy immediately after the collision?

An object of mass $8.0 \mathrm{kg}$ is falling vertically through the air. The drag force acting on the object is $60 \mathrm{N}$. What is the best estimate of the acceleration of the object?

A.  Zero

B.  $2.5 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $7.5 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $10 \mathrm{m} {\mathrm{s}}^{-2}$

An object of mass $1 \mathrm{kg}$ is thrown downwards from a height of $20 \mathrm{m}$. The initial speed of the object is $6 \mathrm{m} {\mathrm{s}}^{-1}$.
The object hits the ground at a speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$. Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$. What is the best estimate of the energy transferred from the object to the air as it falls?

A.  $6 \mathrm{J}$

B.  $18 \mathrm{J}$

C.  $182 \mathrm{J}$

D.  $200 \mathrm{J}$

A body is held in translational equilibrium by three coplanar forces of magnitude $3 \mathrm{N}$, $4 \mathrm{N}$ and $5 \mathrm{N}$. Three statements about these forces are

I.  all forces are perpendicular to each other
II.  the forces cannot act in the same direction
III.  the vector sum of the forces is equal to zero.

Which statements are true?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Show that the radius of the path is about 6 cm.

A body is held in translational equilibrium by three coplanar forces of magnitude $3 \mathrm{N}$, $4 \mathrm{N}$ and $5 \mathrm{N}$. Three statements about these forces are

I.  all forces are perpendicular to each other
II.  the forces cannot act in the same direction
III.  the vector sum of the forces is equal to zero.

Which statements are true?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

Show that the radius of the path is about 6 cm.

Calculate the magnitude of the initial acceleration of the electron.

An object of mass $8.0 \mathrm{kg}$ is falling vertically through the air. The drag force acting on the object is $60 \mathrm{N}$. What is the best estimate of the acceleration of the object?

A.  Zero

B.  $2.5 \mathrm{m} {\mathrm{s}}^{-2}$

C.  $7.5 \mathrm{m} {\mathrm{s}}^{-2}$

D.  $10 \mathrm{m} {\mathrm{s}}^{-2}$

P and Q leave the same point, travelling in the same direction. The graphs show the variation with time $t$ of velocity $v$ for both P and Q.

What is the distance between P and Q when $t=8.0 \mathrm{s}$?

A.  $20 \mathrm{m}$

B.  $40 \mathrm{m}$

C.  $60 \mathrm{m}$

D.  $120 \mathrm{m}$

Calculate the magnitude of the initial acceleration of the electron.

Calculate the magnitude of the initial acceleration of the electron.

P and Q leave the same point, travelling in the same direction. The graphs show the variation with time $t$ of velocity $v$ for both P and Q.

What is the distance between P and Q when $t=8.0 \mathrm{s}$?

A.  $20 \mathrm{m}$

B.  $40 \mathrm{m}$

C.  $60 \mathrm{m}$

D.  $120 \mathrm{m}$

Three forces act on a block which is sliding down a slope at constant speed. $W$ is the weight, $R$ is the reaction force at the surface of the block and $F$ is the friction force acting on the block.

In this situation

A.  there must be an unbalanced force down the plane.

B.  $W=R$.

C.  $F=W$.

D.  the resultant force on the block is zero.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

Determine $v$. State your answer to an appropriate number of significant figures.

Determine $v$. State your answer to an appropriate number of significant figures.

Determine $v$. State your answer to an appropriate number of significant figures.

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

Three forces act on a block which is sliding down a slope at constant speed. $W$ is the weight, $R$ is the reaction force at the surface of the block and $F$ is the friction force acting on the block.

In this situation

A.  there must be an unbalanced force down the plane.

B.  $W=R$.

C.  $F=W$.

D.  the resultant force on the block is zero.

A balloon rises at a steady vertical velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$. An object is dropped from the balloon at a height of $40 \mathrm{m}$ above the ground. Air resistance is negligible. What is the time taken for the object to hit the ground?

A.  $10 \mathrm{s}$

B.  $5 \mathrm{s}$

C.  $4 \mathrm{s}$

D.  $2 \mathrm{s}$

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

The person must not slide down the wall. Show that the minimum angular velocity $\omega$ of the cylinder for this situation is

$\omega =\sqrt{\frac{g}{\mu R}}$

where $\mu$ is the coefficient of static friction between the person and the cylinder.

A balloon rises at a steady vertical velocity of $10 \mathrm{m} {\mathrm{s}}^{-1}$. An object is dropped from the balloon at a height of $40 \mathrm{m}$ above the ground. Air resistance is negligible. What is the time taken for the object to hit the ground?

A.  $10 \mathrm{s}$

B.  $5 \mathrm{s}$

C.  $4 \mathrm{s}$

D.  $2 \mathrm{s}$

An object of mass $m$ strikes a vertical wall horizontally at speed $U$. The object rebounds from the wall horizontally at speed $V$.

What is the magnitude of the change in the momentum of the object?

A.  $0$

B.  $m\left(V-U\right)$

C.  $m\left(U-V\right)$

D.  $m\left(U+V\right)$

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

Draw and label the free-body diagram for the person.

The person must not slide down the wall. Show that the minimum angular velocity $\omega$ of the cylinder for this situation is

$\omega =\sqrt{\frac{g}{\mu R}}$

where $\mu$ is the coefficient of static friction between the person and the cylinder.

Draw and label the free-body diagram for the person.

Draw and label the free-body diagram for the person.

An object of mass $m$ strikes a vertical wall horizontally at speed $U$. The object rebounds from the wall horizontally at speed $V$.

What is the magnitude of the change in the momentum of the object?

A.  $0$

B.  $m\left(V-U\right)$

C.  $m\left(U-V\right)$

D.  $m\left(U+V\right)$

A horizontal force $F$ acts on a sphere. A horizontal resistive force $k{v}^2$ acts on the sphere where $v$ is the speed of the sphere and $k$ is a constant. What is the terminal velocity of the sphere?

A.  $\sqrt{\frac{k}{F}}$

B.  $\frac{k}{F}$

C.  $\frac{F}{k}$

D.  $\sqrt{\frac{F}{k}}$

The person must not slide down the wall. Show that the minimum angular velocity $\omega$ of the cylinder for this situation is

$\omega =\sqrt{\frac{g}{\mu R}}$

where $\mu$ is the coefficient of static friction between the person and the cylinder.

The coefficient of static friction between the person and the cylinder is $0.40$. The radius of the cylinder is $3.5 \mathrm{m}$. The cylinder makes $28$ revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.

The coefficient of static friction between the person and the cylinder is $0.40$. The radius of the cylinder is $3.5 \mathrm{m}$. The cylinder makes $28$ revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.

A horizontal force $F$ acts on a sphere. A horizontal resistive force $k{v}^2$ acts on the sphere where $v$ is the speed of the sphere and $k$ is a constant. What is the terminal velocity of the sphere?

A.  $\sqrt{\frac{k}{F}}$

B.  $\frac{k}{F}$

C.  $\frac{F}{k}$

D.  $\sqrt{\frac{F}{k}}$

An electric motor raises an object of weight $500 \mathrm{N}$ through a vertical distance of $3.0 \mathrm{m}$ in $1.5 \mathrm{s}$. The current in the electric motor is $10 \mathrm{A}$ at a potential difference of $200 \mathrm{V}$. What is the efficiency of the electric motor?

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

The coefficient of static friction between the person and the cylinder is $0.40$. The radius of the cylinder is $3.5 \mathrm{m}$. The cylinder makes $28$ revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.

An electric motor raises an object of weight $500 \mathrm{N}$ through a vertical distance of $3.0 \mathrm{m}$ in $1.5 \mathrm{s}$. The current in the electric motor is $10 \mathrm{A}$ at a potential difference of $200 \mathrm{V}$. What is the efficiency of the electric motor?

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

Determine $v$. State your answer to an appropriate number of significant figures.

Determine $v$. State your answer to an appropriate number of significant figures.

Determine $v$. State your answer to an appropriate number of significant figures.

Calculate the power transferred to the air by the aircraft.

Calculate the power transferred to the air by the aircraft.

Calculate the power transferred to the air by the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The package and string are now released and fall to the ground. The lift force on the aircraft remains unchanged. Calculate the initial acceleration of the aircraft.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

Show that the time taken for the ball to reach the surface of the table is about 0.2 s.

Show that the time taken for the ball to reach the surface of the table is about 0.2 s.

Show that the time taken for the ball to reach the surface of the table is about 0.2 s.

A mass is released from the top of a smooth ramp of height $h$. After leaving the ramp, the mass slides on a rough horizontal surface.

The mass comes to rest in a distance d. What is the coefficient of dynamic friction between the mass and the horizontal surface?

$\text{A. }\frac{gd}{h}$

$\text{B. }\sqrt{\frac{d}{2gh}}$

$\text{C. }\frac{d}{h}$

$\text{D. }\frac{h}{d}$

The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.

Show that the ball will go over the net.

A mass is released from the top of a smooth ramp of height $h$. After leaving the ramp, the mass slides on a rough horizontal surface.

The mass comes to rest in a distance d. What is the coefficient of dynamic friction between the mass and the horizontal surface?

$\text{A. }\frac{gd}{h}$

$\text{B. }\sqrt{\frac{d}{2gh}}$

$\text{C. }\frac{d}{h}$

$\text{D. }\frac{h}{d}$

The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.

Show that the ball will go over the net.

The net is stretched across the middle of the table. The table has a length of 2.74 m and the net has a height of 15.0 cm.

Show that the ball will go over the net.

The minute hand of a clock hanging on a vertical wall has length $L = 30 \text{cm.}$

The minute hand is observed pointing at 12 and then again 30 minutes later when the minute hand is pointing at 6.

What is the average velocity and average speed of point P on the minute hand during this time interval?

Determine the kinetic energy of the ball immediately after the bounce.

A block rests on a rough horizontal plane. A force P is applied to the block and the block moves to the right.

There is a coefficient of friction ${\mu }_{\text{d}}$ giving rise to a frictional force F between the block and the plane. The force P is doubled. Will ${\mu }_{\text{d}}$ and F be unchanged or greater?

The minute hand of a clock hanging on a vertical wall has length $L = 30 \text{cm.}$

The minute hand is observed pointing at 12 and then again 30 minutes later when the minute hand is pointing at 6.

What is the average velocity and average speed of point P on the minute hand during this time interval?

A block rests on a rough horizontal plane. A force P is applied to the block and the block moves to the right.

There is a coefficient of friction ${\mu }_{\text{d}}$ giving rise to a frictional force F between the block and the plane. The force P is doubled. Will ${\mu }_{\text{d}}$ and F be unchanged or greater?

Determine the kinetic energy of the ball immediately after the bounce.

Determine the kinetic energy of the ball immediately after the bounce.

A projectile is launched at an angle above the horizontal with a horizontal component of velocity $V_{\text{h}}$ and a vertical component of velocity $V_{\text{v}}$. Air resistance is negligible. Which graphs show the variation with time of $V_{\text{h}}$ and of $V_{\text{v}}$?

A projectile is launched at an angle above the horizontal with a horizontal component of velocity $V_{\text{h}}$ and a vertical component of velocity $V_{\text{v}}$. Air resistance is negligible. Which graphs show the variation with time of $V_{\text{h}}$ and of $V_{\text{v}}$?

A person with a weight of $600 \text{N}$ stands on a scale in an elevator.

What is the acceleration of the elevator when the scale reads $900 \text{N}$?

A.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

B.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

C.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

D.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

A person with a weight of $600 \text{N}$ stands on a scale in an elevator.

What is the acceleration of the elevator when the scale reads $900 \text{N}$?

A.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

B.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ downwards

C.  $1.5 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

D.  $5.0 {\text{m\hspace{0.05em}s}}^{-2}$ upwards

Player B intercepts the ball when it is at its peak height. Player B holds a paddle (racket) stationary and vertical. The ball is in contact with the paddle for 0.010 s. Assume the collision is elastic.

Calculate the average force exerted by the ball on the paddle. State your answer to an appropriate number of significant figures.

The player’s foot is in contact with the ball for 55 ms. Calculate the average force that acts on the ball due to the football player.

Player B intercepts the ball when it is at its peak height. Player B holds a paddle (racket) stationary and vertical. The ball is in contact with the paddle for 0.010 s. Assume the collision is elastic.

Calculate the average force exerted by the ball on the paddle. State your answer to an appropriate number of significant figures.

Player B intercepts the ball when it is at its peak height. Player B holds a paddle (racket) stationary and vertical. The ball is in contact with the paddle for 0.010 s. Assume the collision is elastic.

Calculate the average force exerted by the ball on the paddle. State your answer to an appropriate number of significant figures.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

The player’s foot is in contact with the ball for 55 ms. Calculate the average force that acts on the ball due to the football player.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

The molar mass of water is 18 g mol⁻¹. Estimate the average speed of the water molecules in the vapor produced. Assume the vapor behaves as an ideal gas.

The player’s foot is in contact with the ball for 55 ms. Calculate the average force that acts on the ball due to the football player.

The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.

The graph shows the variation with distance of a horizontal force acting on an object. The object, initially at rest, moves horizontally through a distance of $50 \text{m}$.

A constant frictional force of $2.0 \text{N}$ opposes the motion. What is the final kinetic energy of the object after it has moved $50 \text{m}$?

A. $100 \text{J}$

B. $500 \text{J}$

C. $600 \text{J}$

D. $1100 \text{J}$

The graph shows the variation with distance of a horizontal force acting on an object. The object, initially at rest, moves horizontally through a distance of $50 \text{m}$.

A constant frictional force of $2.0 \text{N}$ opposes the motion. What is the final kinetic energy of the object after it has moved $50 \text{m}$?

A. $100 \text{J}$

B. $500 \text{J}$

C. $600 \text{J}$

D. $1100 \text{J}$

The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.

The ball leaves the ground at an angle of 22°. The horizontal distance from the initial position of the edge of the ball to the wall is 11 m. Calculate the time taken for the ball to reach the wall.

The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.

The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.

The top of the wall is 2.4 m above the ground. Deduce whether the ball will hit the wall.

Determine H.

Determine H.

Determine H.

An elevator (lift) and its load accelerate vertically upwards.

Which statement is correct in this situation?

A.  The net force on the load is zero.

B.  The tension in the cable is equal but opposite to the combined weight of the elevator and its load.

C.  The normal reaction force on the load is equal but opposite to the force on the elevator from the load.

D.  The elevator and its load are in translational equilibrium.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

An elevator (lift) and its load accelerate vertically upwards.

Which statement is correct in this situation?

A.  The net force on the load is zero.

B.  The tension in the cable is equal but opposite to the combined weight of the elevator and its load.

C.  The normal reaction force on the load is equal but opposite to the force on the elevator from the load.

D.  The elevator and its load are in translational equilibrium.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

The thread makes an angle of 30° with the vertical wall. The ball has a mass of 0.025 kg.

Determine the horizontal force that acts on the ball.

A net force $F$ acts on an object of mass $m$ that is initially at rest. The object moves in a straight line. The variation of $F$ with the distance $s$ is shown.

What is the speed of the object at the distance $s_1$?

A.  $\sqrt{\frac{F_1{s}_1}{2m}}$

B.  $\sqrt{\frac{F_1{s}_1}{m}}$

C.  $\sqrt{\frac{2F_1{s}_1}{m}}$

D.  $\sqrt{\frac{4F_1{s}_1}{m}}$

A net force $F$ acts on an object of mass $m$ that is initially at rest. The object moves in a straight line. The variation of $F$ with the distance $s$ is shown.

What is the speed of the object at the distance $s_1$?

A.  $\sqrt{\frac{F_1{s}_1}{2m}}$

B.  $\sqrt{\frac{F_1{s}_1}{m}}$

C.  $\sqrt{\frac{2F_1{s}_1}{m}}$

D.  $\sqrt{\frac{4F_1{s}_1}{m}}$

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

Draw, on the axes, a graph to show the variation with time of the height of the ball from the instant it rebounds from the floor until the instant it reaches the maximum rebound height. No numbers are required on the axes.

Determine, for particle P, the magnitude and direction of the acceleration at t = 2.0 m s.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

Estimate the loss in the mechanical energy of the ball as a result of the collision with the floor.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

Estimate the loss in the mechanical energy of the ball as a result of the collision with the floor.

Estimate the loss in the mechanical energy of the ball as a result of the collision with the floor.

Determine the average force exerted on the floor by the ball.

Determine the average force exerted on the floor by the ball.

Determine the average force exerted on the floor by the ball.

Outline why a force acts on the airboat due to the fan blade.

Outline why a force acts on the airboat due to the fan blade.

Outline why a force acts on the airboat due to the fan blade.

A car accelerates uniformly from rest to a velocity $v$ during time $t_1$. It then continues at constant velocity $v$ from $t_1$ to time $t_2$.

What is the total distance covered by the car in $t_2$?

A.  $v t_2$

B.  $\frac{1}{2}v\left(t_2-t_1\right)+v t_1$

C.  $\frac{1}{2}v\left(t_2+t_1\right)$

D.  $\frac{1}{2}v t_1+v\left(t_2-t_1\right)$

Show that a mass of about 240 kg of air moves through the fan every second.

A car accelerates uniformly from rest to a velocity $v$ during time $t_1$. It then continues at constant velocity $v$ from $t_1$ to time $t_2$.

What is the total distance covered by the car in $t_2$?

A.  $v t_2$

B.  $\frac{1}{2}v\left(t_2-t_1\right)+v t_1$

C.  $\frac{1}{2}v\left(t_2+t_1\right)$

D.  $\frac{1}{2}v t_1+v\left(t_2-t_1\right)$

Show that a mass of about 240 kg of air moves through the fan every second.

Show that a mass of about 240 kg of air moves through the fan every second.

Outline why a force acts on the airboat due to the fan blade.

Outline why a force acts on the airboat due to the fan blade.

Outline why a force acts on the airboat due to the fan blade.

Show that a mass of about 240 kg of air moves through the fan every second.

Show that a mass of about 240 kg of air moves through the fan every second.

Show that a mass of about 240 kg of air moves through the fan every second.

Show that the tension in the rope is about 5 kN.

Show that the tension in the rope is about 5 kN.

Show that the tension in the rope is about 5 kN.

Show that the tension in the rope is about 5 kN.

Show that the tension in the rope is about 5 kN.

Show that the tension in the rope is about 5 kN.

An object of mass 2.0 kg rests on a rough surface. A person pushes the object in a straight line with a force of 10 N through a distance d.

The resultant force acting on the object throughout d is 6.0 N.

What is the value of the sliding coefficient of friction $\mu$ between the surface and the object and what is the acceleration a of the object?

An object of mass 2.0 kg rests on a rough surface. A person pushes the object in a straight line with a force of 10 N through a distance d.

The resultant force acting on the object throughout d is 6.0 N.

What is the value of the sliding coefficient of friction $\mu$ between the surface and the object and what is the acceleration a of the object?

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Deduce the mass of the airboat.

Show that the kinetic energy of the object is about 0.7 mJ.

Show that the kinetic energy of the object is about 0.7 mJ.

Show that the kinetic energy of the object is about 0.7 mJ.

A block moving with initial speed $v$ is brought to rest, after travelling a distance d, by a frictional force $f$ . A second identical block moving with initial speed u is brought to rest in the same distance d by a frictional force $\frac{f}{2}$. What is u?

A.  $v$

B.  $\frac{v}{\sqrt{2}}$

C.  $\frac{v}{2}$

D.  $\frac{v}{4}$

A ball is thrown upwards at time t = 0. The graph shows the variation with time of the height of the ball. The ball returns to the initial height at time T.

What is the height h at time t ?

A.  $\frac{1}{2}g{t}^2$

B.  $\frac{1}{2}g{T}^2$

C.  $\frac{1}{2}gT\left(T-t\right)$

D.  $\frac{1}{2}gt\left(T-t\right)$

A block moving with initial speed $v$ is brought to rest, after travelling a distance d, by a frictional force $f$ . A second identical block moving with initial speed u is brought to rest in the same distance d by a frictional force $\frac{f}{2}$. What is u?

A.  $v$

B.  $\frac{v}{\sqrt{2}}$

C.  $\frac{v}{2}$

D.  $\frac{v}{4}$

A ball is thrown upwards at time t = 0. The graph shows the variation with time of the height of the ball. The ball returns to the initial height at time T.

What is the height h at time t ?

A.  $\frac{1}{2}g{t}^2$

B.  $\frac{1}{2}g{T}^2$

C.  $\frac{1}{2}gT\left(T-t\right)$

D.  $\frac{1}{2}gt\left(T-t\right)$

A stone is kicked horizontally at a speed of 1.5 m s⁻¹ from the edge of a cliff on one of Jupiter’s moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m. Air resistance is negligible.

What is the magnitude of the displacement of the stone?

A.  7.0 m

B.  5.0 m

C.  4.0 m

D.  3.0 m

A book of mass m lies on top of a table of mass M that rolls freely along the ground. The coefficient of friction between the book and the table is $\mu$. A person is pushing the rolling table.

What is the maximum acceleration of the table so that the book does not slide backwards relative to the table?

A.  $\frac{g}{\mu }$

B.  $\mu g$

C.  $\frac{mg}{M \mu }$

D.  $\frac{m}{M}\mu g$

A book of mass m lies on top of a table of mass M that rolls freely along the ground. The coefficient of friction between the book and the table is $\mu$. A person is pushing the rolling table.

What is the maximum acceleration of the table so that the book does not slide backwards relative to the table?

A.  $\frac{g}{\mu }$

B.  $\mu g$

C.  $\frac{mg}{M \mu }$

D.  $\frac{m}{M}\mu g$

A stone is kicked horizontally at a speed of 1.5 m s⁻¹ from the edge of a cliff on one of Jupiter’s moons. It hits the ground 2.0 s later. The height of the cliff is 4.0 m. Air resistance is negligible.

What is the magnitude of the displacement of the stone?

A.  7.0 m

B.  5.0 m

C.  4.0 m

D.  3.0 m

Which of the formulae represents Newton’s second law?

A.  $\frac{\text{mass}}{\text{volume}}$

B.  $\frac{\text{work}}{\text{displacement}}$

C.  $\frac{\text{change of momentum}}{\text{time}}$

D.  $\text{pressure}\times \text{area}$

Ball 1 is dropped from rest from an initial height $h$. At the same instant, ball 2 is launched vertically upwards at an initial velocity $u$.

At what time are both balls at the same distance above the ground?

A.  $\frac{h}{4u}$

B.  $\frac{h}{2u}$

C.  $\frac{h}{u}$

D.  $\frac{2h}{u}$

The vertical acceleration of the load downwards is 2.4 m s⁻².

Calculate the tension in the string.

The vertical acceleration of the load downwards is 2.4 m s⁻².

Calculate the tension in the string.

The vertical acceleration of the load downwards is 2.4 m s⁻².

Calculate the tension in the string.

Which of the formulae represents Newton’s second law?

A.  $\frac{\text{mass}}{\text{volume}}$

B.  $\frac{\text{work}}{\text{displacement}}$

C.  $\frac{\text{change of momentum}}{\text{time}}$

D.  $\text{pressure}\times \text{area}$

Two masses $m_1$ and $m_2$ are connected by a string over a frictionless pulley of negligible mass. The masses are released from rest. Air resistance is negligible.

Mass $m_2$ accelerates downwards at $\frac{g}{2}$. What is $\frac{m_1}{m_2}$?
A.  $\frac{1}{3}$

B.  $\frac{1}{2}$

C.  2

D.  3

Two masses $m_1$ and $m_2$ are connected by a string over a frictionless pulley of negligible mass. The masses are released from rest. Air resistance is negligible.

Mass $m_2$ accelerates downwards at $\frac{g}{2}$. What is $\frac{m_1}{m_2}$?
A.  $\frac{1}{3}$

B.  $\frac{1}{2}$

C.  2

D.  3

A cart travels from rest along a horizontal surface with a constant acceleration. What is the variation of the kinetic energy E_k of the cart with its distance s travelled? Air resistance is negligible.

Ball 1 is dropped from rest from an initial height $h$. At the same instant, ball 2 is launched vertically upwards at an initial velocity $u$.

At what time are both balls at the same distance above the ground?

A.  $\frac{h}{4u}$

B.  $\frac{h}{2u}$

C.  $\frac{h}{u}$

D.  $\frac{2h}{u}$

A cart travels from rest along a horizontal surface with a constant acceleration. What is the variation of the kinetic energy E_k of the cart with its distance s travelled? Air resistance is negligible.

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

A projectile is launched with a velocity $u$ at an angle $\theta$ to the horizontal. It reaches a maximum height $s$. What is the time taken to reach the maximum height?

A.  $\frac{2s}{u \cos \theta }$

B.  $\frac{2s}{g}$

C.  $\frac{u \cos \theta }{g}$

D.  $\frac{u \sin \theta }{g}$

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

Show that the speed of the load when it hits the floor is about 2.1 m s⁻¹.

A projectile is launched with a velocity $u$ at an angle $\theta$ to the horizontal. It reaches a maximum height $s$. What is the time taken to reach the maximum height?

A.  $\frac{2s}{u \cos \theta }$

B.  $\frac{2s}{g}$

C.  $\frac{u \cos \theta }{g}$

D.  $\frac{u \sin \theta }{g}$

What is the definition of the SI unit for a force?

A.  The force required to accelerate, in the direction of the force, a mass of 1 kg at 1 m s⁻²

B.  The force required to accelerate, in the direction of the force, a mass at 1 m s⁻²

C.  The weight of a mass of 0.1 kg

D.  The change in momentum per second

What is the definition of the SI unit for a force?

A.  The force required to accelerate, in the direction of the force, a mass of 1 kg at 1 m s⁻²

B.  The force required to accelerate, in the direction of the force, a mass at 1 m s⁻²

C.  The weight of a mass of 0.1 kg

D.  The change in momentum per second

After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.

After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.

After the load has hit the floor, the box travels a further 0.35 m along the ramp before coming to rest. Determine the average frictional force between the box and the surface of the ramp.

An engine is exerting a horizontal force $F$ on an object that is moving along a horizontal surface at a constant velocity $v$. The mass of the object is $m$ and the coefficient of dynamic friction between the object and the surface is $\mu$.

What is the power of the engine?

A.  $\frac{Fv}{\mu }$

B.  $\mu Fv$

C.  $\frac{mgv}{\mu }$

D.  $\mu mgv$

An engine is exerting a horizontal force $F$ on an object that is moving along a horizontal surface at a constant velocity $v$. The mass of the object is $m$ and the coefficient of dynamic friction between the object and the surface is $\mu$.

What is the power of the engine?

A.  $\frac{Fv}{\mu }$

B.  $\mu Fv$

C.  $\frac{mgv}{\mu }$

D.  $\mu mgv$

Estimate, using the graph, the maximum height of the bottle.

Determine the energy transferred to the air during the first 3.0 s of motion. State your answer to an appropriate number of significant figures.

Determine the energy transferred to the air during the first 3.0 s of motion. State your answer to an appropriate number of significant figures.

Determine the energy transferred to the air during the first 3.0 s of motion. State your answer to an appropriate number of significant figures.

Describe the energy change that takes place for t > 3.0 s.

Describe the energy change that takes place for t > 3.0 s.

Describe the energy change that takes place for t > 3.0 s.

The polonium nucleus was stationary before the decay.

Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.

The polonium nucleus was stationary before the decay.

Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.

The polonium nucleus was stationary before the decay.

Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.

The polonium nucleus was stationary before the decay.

Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.

The polonium nucleus was stationary before the decay.

Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.

The polonium nucleus was stationary before the decay.

Show, by reference to the momentum of the particles, that the kinetic energy of the alpha particle is much greater than the kinetic energy of the lead nucleus.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

Estimate, using the graph, the maximum height of the bottle.

A ball is projected at an angle to the horizonal on Earth reaching a maximum height H and a maximum range R. The same ball is projected at the same angle and speed on a planet where the acceleration due to gravity is three times that on Earth. Resistance effects are negligible.

What is the maximum range and the maximum height reached on that planet?

A ball is projected at an angle to the horizonal on Earth reaching a maximum height H and a maximum range R. The same ball is projected at the same angle and speed on a planet where the acceleration due to gravity is three times that on Earth. Resistance effects are negligible.

What is the maximum range and the maximum height reached on that planet?

A variable force with a maximum F_max is applied to an object over a time interval T. The object has a mass m and is initially at rest.

What is the speed of the object at time T?

A.  $\frac{F_{\max }T}{2m}$

B.  $\frac{F_{\max }T}{m}$

C.  F_maxTm

D.  2F_maxTm

A variable force with a maximum F_max is applied to an object over a time interval T. The object has a mass m and is initially at rest.

What is the speed of the object at time T?

A.  $\frac{F_{\max }T}{2m}$

B.  $\frac{F_{\max }T}{m}$

C.  F_maxTm

D.  2F_maxTm

A rocket travels a distance of 3 km in 10 s.

What is the order of magnitude of $\frac{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{rocket}}{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum}}$?

A.  −5

B.  −6

C.  −7

D.  −8

A rocket travels a distance of 3 km in 10 s.

What is the order of magnitude of $\frac{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{the} \mathrm{rocket}}{\mathrm{the} \mathrm{speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{a} \mathrm{vacuum}}$?

A.  −5

B.  −6

C.  −7

D.  −8

An object is released from rest at X and slides to Y. The vertical distance between X and Y is 10 m. During the motion, 20 % of the object’s initial gravitational potential energy is lost as friction.

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

An object is released from rest at X and slides to Y. The vertical distance between X and Y is 10 m. During the motion, 20 % of the object’s initial gravitational potential energy is lost as friction.

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

An object is released from rest at X and slides to Y. The vertical distance between X and Y is 10 m. During the motion, 20 % of the object’s initial gravitational potential energy is lost as friction.

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

An object is released from rest at X and slides to Y. The vertical distance between X and Y is 10 m. During the motion, 20 % of the object’s initial gravitational potential energy is lost as friction.

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

A mass on the end of a string is rotating on a frictionless table in circular motion of radius R₁ and undergoes an angular displacement of θ in time t.

The string tension is kept constant, but the angular displacement of the mass is increased to 2θ in time t. The radius of the motion changes to R₂.

What is R₂?

A.  $\frac{R_1}{4}$

B.  2R₁

C.  4R₁

D.  R₁ × R₁

A spring of negligible mass is compressed and placed between two stationary masses m and M. The mass of M is twice that of m. The spring is released so that the masses move in opposite directions.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} m}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} M}$?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

A mass on the end of a string is rotating on a frictionless table in circular motion of radius R₁ and undergoes an angular displacement of θ in time t.

The string tension is kept constant, but the angular displacement of the mass is increased to 2θ in time t. The radius of the motion changes to R₂.

What is R₂?

A.  $\frac{R_1}{4}$

B.  2R₁

C.  4R₁

D.  R₁ × R₁

A mass on the end of a string is rotating on a frictionless table in circular motion of radius R₁ and undergoes an angular displacement of θ in time t.

The string tension is kept constant, but the angular displacement of the mass is increased to 2θ in time t. The radius of the motion changes to R₂.

What is R₂?

A.  $\frac{R_1}{4}$

B.  2R₁

C.  4R₁

D.  R₁ × R₁

A spring of negligible mass is compressed and placed between two stationary masses m and M. The mass of M is twice that of m. The spring is released so that the masses move in opposite directions.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} m}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} M}$?

A.  $\frac{1}{2}$

B.  1

C.  2

D.  4

A mass on the end of a string is rotating on a frictionless table in circular motion of radius R₁ and undergoes an angular displacement of θ in time t.

The string tension is kept constant, but the angular displacement of the mass is increased to 2θ in time t. The radius of the motion changes to R₂.

What is R₂?

A.  $\frac{R_1}{4}$

B.  2R₁

C.  4R₁

D.  R₁ × R₁

Draw and label on diagram B the forces acting on the sphere just after it has been released.

Draw and label on diagram B the forces acting on the sphere just after it has been released.

Draw and label on diagram B the forces acting on the sphere just after it has been released.

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A car travels clockwise around a circular track of radius R. What is the magnitude of displacement from X to Y?

A.  $R\frac{3\pi }{2}$

B.  $R\frac{\pi }{2}$

C.  $R\sqrt{2}$

D.  $R$

A stone of mass m is projected vertically upwards with speed u from the top of a cliff. The speed of the stone when it is just about to hit the ground is v.

What is the magnitude of the change in momentum of the stone?

A.  $m\left(\frac{v+u}{2}\right)$

B.  $m\left(\frac{v-u}{2}\right)$

C.  $m(v+u)$

D.  $m(v-u)$

A stone of mass m is projected vertically upwards with speed u from the top of a cliff. The speed of the stone when it is just about to hit the ground is v.

What is the magnitude of the change in momentum of the stone?

A.  $m\left(\frac{v+u}{2}\right)$

B.  $m\left(\frac{v-u}{2}\right)$

C.  $m(v+u)$

D.  $m(v-u)$

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A car accelerates uniformly. The car passes point X at time t₁ with velocity v₁ and point Y at time t₂ with velocity v₂. The distance XY is s.

The following expressions are proposed for the magnitude of its acceleration a:

I.    $a=\frac{2s}{{(t_2-t_1)}^2}$

II.   $a=\frac{{v_2}^2-{v_1}^2}{2s}$

III.  $a=\frac{v_2-v_1}{t_2-t_1}$

Which is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

A ball attached to a string is made to rotate with constant speed along a horizontal circle. The string is attached to the ceiling and makes an angle of θ ° with the vertical. The tension in the string is T.

What is correct about the horizontal component and vertical component of the net force on the ball?

A ball attached to a string is made to rotate with constant speed along a horizontal circle. The string is attached to the ceiling and makes an angle of θ ° with the vertical. The tension in the string is T.

What is correct about the horizontal component and vertical component of the net force on the ball?

A ball attached to a string is made to rotate with constant speed along a horizontal circle. The string is attached to the ceiling and makes an angle of θ ° with the vertical. The tension in the string is T.

What is correct about the horizontal component and vertical component of the net force on the ball?

A ball attached to a string is made to rotate with constant speed along a horizontal circle. The string is attached to the ceiling and makes an angle of θ ° with the vertical. The tension in the string is T.

What is correct about the horizontal component and vertical component of the net force on the ball?