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

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

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

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

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

A. E_p

B. $\frac{E_p}{2}$

C. $\frac{E_p}{4}$

D. $\frac{E_p}{8}$

A horizontal spring of spring constant k and negligible mass is compressed through a distance y from its equilibrium length. An object of mass m that moves on a frictionless surface is placed at the end of the spring. The spring is released and returns to its equilibrium length.

What is the speed of the object just after it leaves the spring?

A.  $y\sqrt{\frac{k}{m}}$

B.  $y\sqrt{\frac{m}{k}}$

C.  $y\frac{k}{m}$

D.  $y\frac{m}{k}$

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

A.   $\frac{x}{4}$

B.   $\frac{x}{2}$

C.   $\frac{x}{\sqrt{2}}$

D.   $x\sqrt{2}$

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

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

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

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

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

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

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

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

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

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

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

Determine, 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.

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

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

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?

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

From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is 12 m s^–1.

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 cable is pulled by an electric motor. The motor has an overall efficiency of 23 %. Determine the average power input to the motor.

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

A 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. $1100 \text{J}$

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

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

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

A.     $\frac{3}{4}$

B.     $\frac{4}{3}$

C.     $\frac{9}{16}$

D.     $\frac{16}{9}$

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

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

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

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

Calculate the power transferred to the air by the aircraft.

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 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

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

Outline why this force does no work on the Moon.

Outline why this force does no work on Phobos.

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

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

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

The plutonium nucleus is at rest when it decays.

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

The plutonium nucleus is at rest when it decays.

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

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.