A.2 Forces and momentum

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

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.  $\frac{3}{4}\rho$

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.

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

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.

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

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.

Predict whether the collision is elastic.

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.

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.

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

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

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

Determine v_A. State the answer in terms of v.

Determine v_A. State the answer in terms of v.

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

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.

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

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

Deduce whether this collision is elastic.

Deduce whether this collision is elastic.

Deduce whether this collision is elastic.

Determine the recoil velocity of the cannon.

Determine the recoil velocity of the cannon.

Determine the recoil velocity of the cannon.

Calculate the initial kinetic energy of the cannon.

Calculate the initial kinetic energy of the cannon.

Calculate the initial kinetic energy of the cannon.

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

Show that the collision is elastic.

Show that the collision is elastic.

Show that the collision is elastic.

Show that the collision is elastic.

Show that the collision is elastic.

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 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 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 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 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 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).

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).

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).

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.

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.

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.

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.

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.

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.

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

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

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.  $\mu mgv$

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

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 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 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.

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.

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 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 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 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

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.  $\sqrt{5^3}$

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.

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

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.

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.

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.

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 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 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 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 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 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 $W$

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 $W$

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 $W$

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 $W$

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 $W$

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 $W$

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 $W$

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 $W$

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 $W$

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 $W$

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

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 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

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?

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

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

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?

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?

Outline why this force does no work on Phobos.

Outline why this force does no work on Phobos.

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 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 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.

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.

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.

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.

Outline why this force does no work on the Moon.

Outline why this force does no work on the Moon.

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.

Calculate F.

Calculate F.

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 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. $\frac{g}{\omega r^2}$

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

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 speed of the ball as it leaves the racket.

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

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.

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

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

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

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

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

Calculate the time for one complete revolution.

Calculate the time for one complete revolution.

Calculate the time for one complete revolution.

Calculate the magnitude of the initial acceleration of the electron.

Calculate the magnitude of the initial acceleration of the electron.

Calculate the magnitude of the initial acceleration of the electron.

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

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

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.  $\sqrt{\frac{F}{k}}$

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.  $\sqrt{\frac{F}{k}}$

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.  $\frac{m{v}^2}{gr}$

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.  $\frac{m{v}^2}{gr}$

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 $2m$ 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 $8.0 \mathrm{kg}$ 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.

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.

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.  $m\left(U+V\right)$

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.  $m\left(U+V\right)$

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.

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.

Determine the terminal velocity of the sphere.

Determine the terminal velocity of the sphere.

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

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

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 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 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 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?

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.  $\frac{1}{F}$

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 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

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. $1100 \text{J}$

Calculate the value of the centripetal force.

Calculate the value of the centripetal force.

Calculate the value of the centripetal force.

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.

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.

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’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.

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.

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.

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 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

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.

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 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.  $\sqrt{\frac{4F_1{s}_1}{m}}$

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.  $\frac{m}{M}\mu g$

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

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 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 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.  $\frac{v}{4}$

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

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 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

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

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?

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.

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.

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.

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.

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.

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?

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?

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 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 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 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 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 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 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

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

determine the tension in the string.

Show that the collision is elastic.

Show that the collision is elastic.

Show that the collision is elastic.

Show that the collision is elastic.

Show that the collision is elastic.

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 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 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 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 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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.