A. Space, time and motion

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

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.

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 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.

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 time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

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

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

Show that the tennis ball passes over the net.

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

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.

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

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.

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.  $120 \mathrm{m}$

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.  $200 \mathrm{J}$

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

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 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 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 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 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.  $2 \mathrm{s}$

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 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.  $\frac{1}{2}gt\left(T-t\right)$

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 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.  $\frac{u \sin \theta }{g}$

Calculate d.

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

Estimate the acceleration of the bottle when it is at its maximum height.

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

Estimate the acceleration of the bottle when it is at its maximum height.

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 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 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 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 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 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

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

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.

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

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.

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 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.

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 time it takes the tennis ball to reach the net.

Show that the tennis ball passes over the net.

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

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

Show that the tennis ball passes over the net.

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

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

Show that the tennis ball passes over the net.

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

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

Show that the tennis ball passes over the net.

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

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 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.

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

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.

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.  $120 \mathrm{m}$

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.  $200 \mathrm{J}$

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

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.

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

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 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 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 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 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.  $2 \mathrm{s}$

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 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.  $\frac{1}{2}gt\left(T-t\right)$

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 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.  $\frac{u \sin \theta }{g}$

Calculate d.

Calculate d.

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

Estimate the acceleration of the bottle when it is at its maximum height.

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

Estimate the acceleration of the bottle when it is at its maximum height.

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

Estimate the acceleration of the bottle when it is at its maximum height.

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

Estimate the acceleration of the bottle when it is at its maximum height.

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 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 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 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 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 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 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?

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.  $\frac{m}{M}\mu g$

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

Calculate the tension in the string.

The radius of the pulley is 2.5 cm. Calculate the angular speed of rotation of the pulley as the load hits the floor. State your answer to an appropriate number of significant figures.

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.

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

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

Outline why this force does no work on the Moon.

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

Calculate the time for one complete revolution.

The magnitude of the resultant of two forces acting on a body is 12 N. Which pair of forces acting on the body can combine to produce this resultant?

A.  1 N and 2 N

B.  1 N and 14 N

C.  5 N and 6 N

D.  6 N and 7 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

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

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. $\frac{g}{\omega r^2}$

Outline why this force does no work on Phobos.

The orbital period T of a moon orbiting a planet of mass M is given by

$$\frac{R^3}{T^2}=kM$$

where R is the average distance between the centre of the planet and the centre of the moon.

Show that $k=\frac{G}{4{\pi }^2}$

The following data for the Mars–Phobos system and the Earth–Moon system are available:

Mass of Earth = 5.97 × 10²⁴ kg

The Earth–Moon distance is 41 times the Mars–Phobos distance.

The orbital period of the Moon is 86 times the orbital period of Phobos.

Calculate, in kg, the mass of Mars.

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?

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?

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

A particle of mass 0.02 kg moves in a horizontal circle of diameter 1 m with an angular velocity of 3$\pi$ rad s^-1. 

What is the magnitude and direction of the force responsible for this motion?

Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period T. When P is at the top of its motion, Q is at the bottom of its motion.

What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?

A. $\frac{T}{4}$

B. $\frac{T}{2}$

C. $\frac{3T}{4}$

D. T

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.

Calculate the average force exerted by the racquet 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.  $\sqrt{\frac{4F_1{s}_1}{m}}$

Calculate the value of the centripetal force.

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 player kicks the ball again. It rolls along the ground without sliding with a horizontal velocity of $1.40 {\text{m\hspace{0.05em}s}}^{-1}$. The radius of the ball is $0.11 \text{m}$. Calculate the angular velocity of the ball. State an appropriate SI unit for your answer.

Calculate the magnitude of the initial acceleration of the electron.

Determine the terminal velocity of the sphere.

Determine the force exerted by the spring on the sphere when the sphere is at rest.

Calculate F.

Mass $M$ is attached to one end of a string. The string is passed through a hollow tube and mass $m$ is attached to the other end. Friction between the tube and string is negligible.

Mass $m$ travels at constant speed $v$ in a horizontal circle of radius $r$. What is mass $M$?

A.  $\frac{m{v}^2}{r}$

B.  $m{v}^{2}rg$

C.  $\frac{mg{v}^2}{r}$

D.  $\frac{m{v}^2}{gr}$

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

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.  $10 \mathrm{m} {\mathrm{s}}^{-2}$

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 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

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.  $m\left(U+V\right)$

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.

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

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?

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

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

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

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

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

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. $1100 \text{J}$

An object moves in a circle of constant radius. Values of the centripetal force $F$ are measured for different values of angular velocity $\omega$. A graph is plotted with $\omega$ on the $x$-axis. Which quantity plotted on the $y$-axis will produce a straight-line graph?

A.  $\sqrt{F}$

B.  $F$

C.  $F^2$

D.  $\frac{1}{F}$

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?

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 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

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

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.

A ball of mass (50 ± 1) g is moving with a speed of (25 ± 1) m s⁻¹. What is the fractional uncertainty in the momentum of the ball?

A.  0.02

B.  0.04

C.  0.06

D.  0.08

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 satellite is orbiting Earth in a circular path at constant speed. Three statements about the resultant force on the satellite are:

I.   It is equal to the gravitational force of attraction on the satellite.
II.  It is equal to the mass of the satellite multiplied by its acceleration.
III. It is equal to the centripetal force on the satellite.

Which combination of statements is correct?

A.  I and II only

B.  I and III only

C.  II and III only

D.  I, II and III

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

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.  $\mu mgv$

Two masses $\text{M}$ and $\text{m}$ are connected by a string that runs without friction through a stationary tube. Mass $\text{m}$ rotates at constant speed in a horizontal circle of radius 0.25 m. The weight of $\text{M}$ provides the centripetal force for the motion of $\text{m}$. The time period for the rotation of m is 0.50 s.

What is $\frac{\text{mass of M}}{\text{mass of m}}$?

A.  1

B.  2

C.  4

D.  8

The scale diagram shows the weight W of the mass at an instant when the rod is horizontal.

Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.

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.

A person stands in an elevator (lift). The total mass of the person and the elevator is 800 kg. The elevator accelerates upward at 2.0 m s⁻².

What is the tension in the cable?

A.  1.6 kN

B.  6.4 kN

C.  8.0 kN

D.  9.6 kN

A bird of weight $W$ sits on a thin rope at its midpoint. The rope is almost horizontal and has negligible mass.

The tension in the rope is

A.  less than $\frac{W}{2}$

B.  equal to $\frac{W}{2}$

C.  between $\frac{W}{2}$ and $W$

D.  greater than $W$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

A person stands in an elevator (lift). The total mass of the person and the elevator is 800 kg. The elevator accelerates upward at 2.0 m s⁻².

What is the tension in the cable?

A.  1.6 kN

B.  6.4 kN

C.  8.0 kN

D.  9.6 kN

A bird of weight $W$ sits on a thin rope at its midpoint. The rope is almost horizontal and has negligible mass.

The tension in the rope is

A.  less than $\frac{W}{2}$

B.  equal to $\frac{W}{2}$

C.  between $\frac{W}{2}$ and $W$

D.  greater than $W$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

Determine the largest magnitude of F for which the block and the object do not move relative to each other.

Show that the electric charge on the oil drop is given by

$q=\frac{{\rho }_{o}gV}{E}$

where ${\rho }_o$ is the density of oil and $V$ is the volume of the oil drop.

Ball 1 collides with an initially stationary ball 2 of the same mass. After the collision, the balls move with speeds $v_1$ and $v_2$. Their velocities make angles ${\theta }_1$ and ${\theta }_2$ with the original direction of motion of ball 1.

What is $\frac{v_1}{v_2}$

A.  $\frac{\sin {\theta }_2}{\sin {\theta }_1}$

B.  $\frac{\sin {\theta }_1}{\sin {\theta }_2}$

C.  $\frac{\cos {\theta }_2}{\cos {\theta }_1}$

D.  $\frac{\cos {\theta }_1}{\cos {\theta }_2}$

A body of height 40 cm and uniform cross-sectional area floats in water. 10 cm of the height of the body remains above the water line.

The density of water is $\rho$. What is the density of the body?

A.  $\frac{1}{4}\rho$

B.  $\frac{1}{3}\rho$

C.  $\frac{2}{3}\rho$

D.  $\frac{3}{4}\rho$

Hence, calculate the vertical component of the velocity of ball B after the collision.

Determine the angle θ that the velocity of ball B makes with the initial direction of motion of ball A.

Predict whether the collision is elastic.

No unbalanced external forces act on the system of the curling stones. Outline why the momentum of the system does not change during the collision.

Show that $v_{\text{B}}=\frac{\sin 70°}{\sin 20°}{v}_A$.

Determine v_A. State the answer in terms of v.

Calculate the component of momentum of the first curling stone perpendicular to the initial direction.

Calculate the velocity component of the first curling stone in the initial direction.

Deduce whether this collision is elastic.

Determine the recoil velocity of the cannon.

Calculate the initial kinetic energy of the cannon.

determine the tension in the string.

Show that the collision is elastic.

The coefficient of dynamic friction between the block and the rough surface is 0.400. 

Estimate the distance travelled by the block on the rough surface until it stops.

The mass of the charge q is 0.025 kg.

Calculate the angular frequency of the oscillations using the data in (a)(ii) and the expression in (b)(i).

determine the tension in the string.

Show that the collision is elastic.

The coefficient of dynamic friction between the block and the rough surface is 0.400. 

Estimate the distance travelled by the block on the rough surface until it stops.

The mass of the bottle is 27 g and it is in contact with the ground for 85 ms.

Determine the average force exerted by the ground on the bottle. Give your answer to an appropriate number of significant figures.

The mass of the bottle is 27 g and it is in contact with the ground for 85 ms.

Determine the average force exerted by the ground on the bottle. Give your answer to an appropriate number of significant figures.

After a second bounce, the bottle rotates about its centre of mass. The bottle rotates at 0.35 revolutions per second.

The centre of mass of the bottle is halfway between the base and the top of the bottle. Assume that the velocity of the centre of mass is zero.

Calculate the linear speed of the top of the bottle.

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 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 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 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.

The total friction in the system acting on the tram is equivalent to an opposing force of 750 N.

For one particular journey, the tram is full of passengers.

Estimate the maximum speed v of the tram as it leaves the lower station.

A person stands in an elevator (lift). The total mass of the person and the elevator is 800 kg. The elevator accelerates upward at 2.0 m s⁻².

What is the tension in the cable?

A.  1.6 kN

B.  6.4 kN

C.  8.0 kN

D.  9.6 kN

A bird of weight $W$ sits on a thin rope at its midpoint. The rope is almost horizontal and has negligible mass.

The tension in the rope is

A.  less than $\frac{W}{2}$

B.  equal to $\frac{W}{2}$

C.  between $\frac{W}{2}$ and $W$

D.  greater than $W$

Planets X and Y orbit the same star.

The average distance between planet X and the star is five times greater than the average distance between planet Y and the star.

What is $\frac{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{X}}{\mathrm{orbital} \mathrm{period} \mathrm{of} \mathrm{planet} \mathrm{Y}}$?

A.  $\sqrt[3]{5}$

B.  $\sqrt{5}$

C.  $\sqrt[3]{5^2}$

D.  $\sqrt{5^3}$

A person stands in an elevator (lift). The total mass of the person and the elevator is 800 kg. The elevator accelerates upward at 2.0 m s⁻².

What is the tension in the cable?

A.  1.6 kN

B.  6.4 kN

C.  8.0 kN

D.  9.6 kN

A bird of weight $W$ sits on a thin rope at its midpoint. The rope is almost horizontal and has negligible mass.

The tension in the rope is

A.  less than $\frac{W}{2}$

B.  equal to $\frac{W}{2}$

C.  between $\frac{W}{2}$ and $W$