A.3 Work, energy and power

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

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.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

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.

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.  $\mu mgv$

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

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

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

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

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

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

The polonium nucleus was stationary before the decay.

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

The polonium nucleus was stationary before the decay.

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

The polonium nucleus was stationary before the decay.

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

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An object is released from rest in a vacuum at a height $H$ above the Earth’s surface.

As the object falls it passes a point at a height of 0.75$H$ above the surface.

What is $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{the} \mathrm{object} \mathrm{at} \mathrm{a} \mathrm{height} \mathrm{of} 0.75H}{\text{gravitational potential energy of the object at a height of} H}$ ?

A.  $\frac{1}{16}$

B.  $\frac{1}{4}$

C.  $\frac{9}{16}$

D.  $\frac{3}{4}$

An insulated tube is filled with a large number n of lead spheres, each of mass m. The tube is inverted s times so that the spheres completely fall through an average distance L each time. The temperature of the spheres is measured before and after the inversions and the resultant change in temperature is ΔT.

What is the specific heat capacity of lead?

A. $\frac{sgL}{nm\mathrm{\Delta }T}$

B. $\frac{sgL}{\mathrm{\Delta }T}$

C. $\frac{sgL}{n\mathrm{\Delta }T}$

D. $\frac{gL}{m\mathrm{\Delta }T}$

An insulated tube is filled with a large number n of lead spheres, each of mass m. The tube is inverted s times so that the spheres completely fall through an average distance L each time. The temperature of the spheres is measured before and after the inversions and the resultant change in temperature is ΔT.

What is the specific heat capacity of lead?

A. $\frac{sgL}{nm\mathrm{\Delta }T}$

B. $\frac{sgL}{\mathrm{\Delta }T}$

C. $\frac{sgL}{n\mathrm{\Delta }T}$

D. $\frac{gL}{m\mathrm{\Delta }T}$

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

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

A. 5 kJ

B. 4.9 kJ

C. 4.88 kJ

D. 4.880 kJ

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

A. 5 kJ

B. 4.9 kJ

C. 4.88 kJ

D. 4.880 kJ

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.

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

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

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

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

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

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

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 power delivered to the ball during the impact.

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

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

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

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

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

Estimate the average speed of the helium atoms in the container.

Estimate the average speed of the helium atoms in the container.

Estimate the average speed of the helium atoms in the container.

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

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

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

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

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

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

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

A. $\frac{E}{16}$

B. $\frac{E}{4}$

C. $\frac{3E}{4}$

D. $\frac{15E}{16}$

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

A. $\frac{E}{16}$

B. $\frac{E}{4}$

C. $\frac{3E}{4}$

D. $\frac{15E}{16}$

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

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

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

Explain why the kinetic energy of the proton is constant.

Explain why the kinetic energy of the proton is constant.

Explain why the kinetic energy of the proton is constant.

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

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

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

A bicycle of mass $M$ comes to rest from speed $v$ using the back brake. The brake has a specific heat capacity of $c$ and a mass $m$. Half of the kinetic energy is absorbed by the brake.

What is the change in temperature of the brake?

A.  $\frac{M{v}^2}{4mc}$

B.  $\frac{M{v}^2}{2mc}$

C.  $\frac{m{v}^2}{4Mc}$

D.  $\frac{m{v}^2}{2Mc}$

A bicycle of mass $M$ comes to rest from speed $v$ using the back brake. The brake has a specific heat capacity of $c$ and a mass $m$. Half of the kinetic energy is absorbed by the brake.

What is the change in temperature of the brake?

A.  $\frac{M{v}^2}{4mc}$

B.  $\frac{M{v}^2}{2mc}$

C.  $\frac{m{v}^2}{4Mc}$

D.  $\frac{m{v}^2}{2Mc}$

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

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

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

A.  $17 \%$

B.  $38 \%$

C.  $50 \%$

D.  $75 \%$

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

A.  $6 \mathrm{J}$

B.  $18 \mathrm{J}$

C.  $182 \mathrm{J}$

D.  $200 \mathrm{J}$

An object of mass $1 \mathrm{kg}$ 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.  $200 \mathrm{J}$

Calculate the power transferred to the air by the aircraft.

Calculate the power transferred to the air by the aircraft.

Calculate the power transferred to the air by the aircraft.

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?

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

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

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

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

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. $1100 \text{J}$

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

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

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

The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m⁻².

A measure of the efficiency of a photovoltaic cell is the ratio

$\frac{\text{energy available every second to the external circuit}}{\text{energy arriving every second at the photovoltaic cell surface}}.$

Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.

The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m⁻².

A measure of the efficiency of a photovoltaic cell is the ratio

$\frac{\text{energy available every second to the external circuit}}{\text{energy arriving every second at the photovoltaic cell surface}}.$

Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.

The maximum intensity of sunlight incident on the photovoltaic cell at the place on the Earth’s surface is 680 W m⁻².

A measure of the efficiency of a photovoltaic cell is the ratio

$\frac{\text{energy available every second to the external circuit}}{\text{energy arriving every second at the photovoltaic cell surface}}.$

Determine the efficiency of this photovoltaic cell when the intensity incident upon it is at a maximum.

A fuel has mass density $\rho$ and energy density $u$. What mass of the fuel has to be burned to release thermal energy $E$?

A.  $\frac{\rho E}{u}$

B.  $\frac{uE}{\rho }$

C.  $\frac{\rho u}{E}$

D.  $\rho uE$

A fuel has mass density $\rho$ and energy density $u$. What mass of the fuel has to be burned to release thermal energy $E$?

A.  $\frac{\rho E}{u}$

B.  $\frac{uE}{\rho }$

C.  $\frac{\rho u}{E}$

D.  $\rho uE$

Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.

Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.

Show that the energy dissipated in the loop from t = 0 to t = 3.5 s is 0.13 J.

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

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

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

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

A.  $m\left(\frac{v+u}{2}\right)$

B.  $m\left(\frac{v-u}{2}\right)$

C.  $m(v+u)$

D.  $m(v-u)$

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

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

A.  $m\left(\frac{v+u}{2}\right)$

B.  $m\left(\frac{v-u}{2}\right)$

C.  $m(v+u)$

D.  $m(v-u)$

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

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

A.  $m\left(\frac{v+u}{2}\right)$

B.  $m\left(\frac{v-u}{2}\right)$

C.  $m(v+u)$

D.  $m(v-u)$

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

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

A.  $m\left(\frac{v+u}{2}\right)$

B.  $m\left(\frac{v-u}{2}\right)$

C.  $m(v+u)$

D.  $m(v-u)$

A 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 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

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

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

What is the speed of the object at Y?

A.  $\frac{16}{\sqrt{g}}$

B.  $2\sqrt{g}$

C.  $4\sqrt{g}$

D.  $8g$

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

show that the speed of the ball is about 4.3 m s⁻¹.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the maximum height risen by the centre of the ball.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the fraction of the kinetic energy of the bottle that remains after the bounce.

Calculate the energy lost during the collision.

Calculate the energy lost during the collision.

Calculate the energy lost during the collision.

Calculate the energy lost during the collision.