Work, Energy and Power

Which relationship is used in the derivation of the equation shown?

$$\text{power} = \text{force} \times \text{velocity}$$

Options

A   displacement $= \text{velocity} \times \text{time}$
B   force $= \text{mass} \times \text{acceleration}$
C   momentum $= \text{mass} \times \text{velocity}$
D   velocity $= \text{acceleration} \times \text{time}$

A block is released from rest at the top of a slope inclined at an angle $\theta$ to the horizontal. The slope has length $L$ as shown in the diagram.

There are no resistive forces acting on the block.
What is the speed of the block at the bottom of the slope?

Options

A   $4.43\sqrt{L\cos\theta}$
B   $4.43\sqrt{L\sin\theta}$
C   $19.6L\cos\theta$
D   $19.6L\sin\theta$

A skateboarder and her skateboard have a total mass of $70\text{ kg}$. She pushes on the ground with her foot to create a forward force $F$ of $25\text{ N}$ on herself and the skateboard, as shown in the diagram.

The skateboarder and skateboard travel forwards a distance of $0.50\text{ m}$ before the skateboarder lifts her foot from the ground.
What is the work done by $F$ on the skateboarder and skateboard?

Options

A   $13\text{ J}$
B   $50\text{ J}$
C   $340\text{ J}$
D   $360\text{ J}$

A turbine at a hydroelectric power station is situated at a vertical distance of $30\text{ m}$ below the level of the surface of a large lake. The water passes through the turbine at a rate of $340\text{ m}^3$ per minute.
The overall efficiency of the turbine and generator system is $90\%$. The density of water is $1000\text{ kg m}^{-3}$.
What is the useful power output of the power station?

Options

A   $0.15\text{ MW}$
B   $1.5\text{ MW}$
C   $1.7\text{ MW}$
D   $90\text{ MW}$

Leonardo da Vinci proposed a flying machine that would work like a screw to lift the pilot into the air. The ‘screw’ is rotated by the pilot.

The machine and the pilot together have a total mass of $120\text{ kg}$.

Which useful output power must the pilot provide to move vertically upwards at a constant speed of $2.5\text{ m s}^{-1}$?

Options

A   $48\text{ W}$
B   $300\text{ W}$
C   $470\text{ W}$
D   $2900\text{ W}$

An object is falling in a uniform gravitational field.

Which two quantities are sufficient to calculate the change in gravitational potential energy?

Options

A   mass and acceleration of free fall
B   mass and change in vertical displacement
C   weight and acceleration of free fall
D   weight and change in vertical displacement

The points X, Y and Z are on a rough, horizontal surface.

A box P is pushed across the surface from X to Y and then from Y to Z.

The distance from X to Y is $3.0\text{ m}$. The work done against the frictional force in moving the box from X to Y is $150\text{ J}$.

The work done against the frictional force in moving the box from Y to Z is $200\text{ J}$.

An identical box Q is pushed in a straight line from X to Z.

The magnitude of the frictional force between the boxes and the surface is constant.

How much extra work is done against the frictional force in moving P than Q?

Options

A   $100\text{ J}$
B   $250\text{ J}$
C   $350\text{ J}$
D   $600\text{ J}$

The momentum of a car of mass $m$ increases from $p_1$ to $p_2$.

What is the increase in the kinetic energy of the car?

Options

A   $\dfrac{(p_2^2 - p_1)^2}{2m}$
B   $\dfrac{(p_2 - p_1)^2}{2m}$
C   $\dfrac{p_2 - p_1}{2m}$
D   $\dfrac{p_1 - p_2}{2m}$

A parachutist is falling at constant (terminal) velocity.

Which statement is not correct?

Options

A   Gravitational potential energy is converted into kinetic energy of the air.
B   Gravitational potential energy is converted into kinetic energy of the parachutist.
C   Gravitational potential energy is converted into thermal energy of the air.
D   Gravitational potential energy is converted into thermal energy of the parachutist.

An empty cart is moving along a horizontal track at a constant velocity.

Resistive forces acting on the cart are negligible.

A heavy rock is dropped vertically into the cart.

The cart continues to move horizontally with the rock inside.

How does the momentum and kinetic energy of the cart with the rock inside compare with the momentum and kinetic energy of the empty cart?

Options

A   The cart with the rock inside has a smaller momentum and a smaller kinetic energy.
B   The cart with the rock inside has a smaller momentum and the same kinetic energy.
C   The cart with the rock inside has the same momentum and a smaller kinetic energy.
D   The cart with the rock inside has the same momentum and the same kinetic energy.