Work, Energy & Power (AQA A Level Physics)

Trains supply coal to a power station. The table below gives quantities describing the operation of the power station.

	symbol	unit
power station output	P	W
number of trains per day	N
mass of coal on a train	M	kg
energy from 1 kg of coal	J	J
number of seconds in one day	S	s

Which expression gives efficiency of the power station?

Initially, four identical uniform blocks, each of mass m and thickness h, are spread on a table.

How much work is done on the blocks in stacking them on top of one another?

The first column in the table gives four examples of work being done. The second column gives more detail of the action.

Which row is not correct?

	Example	Detail
A	a diver dives from a diving board into a swimming pool	work is done by the diver against gravity as she falls
B	a person pushes a car along a level road	work is done by the person against friction
C	an electron is accelerated towards a positively–charged plate	work is done on the electron by the electric field of the plate
D	a piston is pushed outwards as a gas expands	work is done on the atmosphere by the gas

The data below are taken from a test of a petrol engine for a motor car.

         power output                150kW

         fuel consumption                  20 litres per hour

       energy content of fuel                 40 MJ per litre

Which expression will evaluate the efficiency of the engine?

A weight W hangs from a trolley that runs along a rail. The trolley moves horizontally through a distance p and simultaneously raises the weight through a height q.

As a result, the weight moves through a distance r from X to Y. It starts and finishes at rest.

How much work is done on the weight during this process?

A uniform solid block has weight 500 N, width 0.4 m and height 0.6 m. The block rests on the edge of a step of depth 0.8 m, as shown.

The block is knocked over the edge of the step and rotates through 90° before coming to rest with the 0.6 m edge horizontal.

What is the change in gravitational potential energy of the block?

A body travelling with a speed of 20 m s^–1 has kinetic energy E_k.

If the speed of the body is increased to 80 m s^–1, what is its new kinetic energy?

A concrete cube of side 0.60 m and uniform density 2.0 × 10³ kg m^–3 is lifted 5.0 m vertically by a crane.

What is the change in potential energy of the cube?

A steel ball is falling at constant speed in oil.

Which graph shows the variation with time of the gravitational potential energy E_p and the kinetic energy E_k of the ball?

Car X is travelling at half the speed of car Y. Car X has twice the mass of car Y.

Which statement is correct?

To exit an underground cave network, an electric winch is used to raise a lift containing the cavers back to the surface.  A diagram of the setup is shown below.

The lift and the cavers have a total mass of 400 kg.  The winch raises the lift through a vertical height of 1000 m in 2 minutes.

If the motor is 80% efficient, what is the total power wasted by the winch?

A child on a swing is released from rest at position A.  They were found to be moving at 2.2 m s^–1 at position B.  The mass of the child and the swing is 28 kg.  The rope connecting the swing to the frame is 1.6 m.  The positions A and B are shown below.

There is a constant resistive force acting on the child between A and B.

What is the resistive force acting on the child between A and B?

Water flows from a lake into a turbine that is a vertical distance of 90 m below the lake, as shown.

The mass flow rate of the water is 2400 kg min^–1. The turbine has an efficiency of 75%.

What is the output power of the turbine?

When the 4 kg mass is released from rest at a height of 5 m it falls to the ground pulling the 3 kg mass up the slope.  The rough surface of the ramp provides a constant frictional force of 2 N.

What speed will the 4 kg mass hit the ground?

A stone of mass 1.2 kg is dropped from a height of 15 m above the surface of a thick, oily liquid, as shown below.  The surface of the liquid is 2 m above the ground. 

The resistive force acting on the stone as it falls through the liquid is 150 N. 

What is the speed of the stone when it has travelled 0.5 m through the liquid?

The diagram shows a lift system in which the elevator (mass m₁) is partly counterbalanced by a heavy weight (mass m₂)

At what rate does the motor provide energy to the system when the elevator is rising at a steady speed v? (g = acceleration of free fall)

The diagram shows the design of a water wheel which drives a generator to produce electrical energy. The flow rate of the water is 200 kg s^–1. The generator supplies a current of 32 A at a voltage of 230 V.

Ignoring any changes in kinetic energy of the water, what is the efficiency of the system?

A bungee jumper has 24 kJ of gravitational potential energy at the top of his jump. He is attached to an elastic rope which starts to stretch after a short time of free fall. Assume that energy loss through air resistance is negligible.

	GPE / kJ	EPE / kJ	KE / kJ
Top	24	0	0
Bottom	0	24	0

What are the possible values when the jumper is half–way down?

	GPE / kJ	EPE / kJ	KE / kJ
A	12	10	2
B	12	8	4
C	8	8	8
D	12	2	10

An engineer is preparing to install a new escalator for an underground train company.  For their calculations, they assume that the average mass of a passenger using the escalator is 70 kg. 

The escalator will be installed at an angle of 30^o to the horizontal and lift people to a vertical height of 15 m in 10 seconds, as shown below.

If all of the passengers stand still on the escalator, 75 people can step on at the bottom and off at the top in each minute. 

When the escalator is fully laden with passengers the motor driving the escalator is 80% efficient and the frictional force acting on the escalator system 15 kN.

What is the input power needed to operate the motor?

Wind turbines are becoming increasing popular for generating electricity.  On average they have are 70% efficient at producing electrical energy.  In one particular design of wind turbine the blades rotate about a horizontal axis and sweep out at an area of 1400 m².

On a particular day the horizontal axis of the turbine blades points directly into the wind, as shown below, and the wind speed is 15 m s^–1.  The air is slowed to 13 m s^–1 after passing through the turbine blades.  

How many wind turbines would be needed to produce the same amount of electricity as a 1000 GW power station?

Assume that there are no frictional forces in the turbine and take the density of air to be is 1.2 kg m^–3