Work done & energy transfer

A force F moves through a distance x in the direction of F.

In which row is the work done by the force 1 J ?

A spring is compressed by a force F. The spring has stiffness k and its length changes by Δ L during the compression. When the force is removed the spring returns to its original length in time t.

What is the average power developed by the spring as it returns to its original length?

In 2021 the world land speed record was 1230 km h⁻¹. This was the average speed achieved by a jet-powered car in two runs. Each run was measured over a distance of 1.61 km.

The average speed for one of these runs was 343 m s⁻¹.

Calculate, in s, the time taken for the car to complete the other run.

Engineers are designing a new jet-powered car to break this record.

Figure 1 shows the variation of speed with distance for the car, as predicted by the engineers.

The car reaches its maximum acceleration when it is 5600 m from the start. At this point the mass of the car is 6.50 × 10³ kg.

Determine the kinetic energy of the car at its maximum acceleration.

At any point on the graph in Figure 1, the acceleration is given by:

acceleration = speed × gradient of line

When the car is at its maximum acceleration, the power input to the jet engines is 640 MW.

Calculate the percentage of the input power used to accelerate the car at its maximum acceleration.

Scientists recommend that the average deceleration of the driver of the car should be less than 3 g.

Deduce whether the average deceleration is less than 3 g.

Mechanical power

An electric motor lifts a load of weight W through a vertical height h in time t. The potential difference across the motor is V and the current in it is I.

What is the efficiency of the motor?

Safety barriers are used on UK motorways to prevent vehicles crossing from one carriageway to the other carriageway. The barriers also absorb some of the kinetic energy of a vehicle and deflect vehicles along the barrier.

The standard test of a safety barrier uses a vehicle that contains dummies. The total mass of the vehicle and its contents is 1.5 × 10³ kg and its initial speed is 110 km h^–1

Show that the initial kinetic energy of the test vehicle is 700 kJ.

The test vehicle hits a steel safety barrier at an angle of 20°, as shown in Figure 7.

Calculate the component of the momentum of the test vehicle in a direction along the line of the safety barrier. Give an appropriate unit for your answer.

Immediately after the collision, the test vehicle moves along the safety barrier with no change in its momentum in this direction.

Show that the kinetic energy lost in the collision is about 80 kJ.

The steel safety barrier deforms during the collision. For the barrier to pass the test, the test vehicle should not move more than 1.5 m towards the other carriageway.

The barrier can apply an average force of 60 kN at right angles to the carriageway.

Deduce whether the safety barrier will pass the test.

A different safety barrier uses a solid concrete wall which does not deform. The same standard test is carried out on a concrete wall.

Discuss which type of barrier would cause less damage to the dummies in the test.

An electric vehicle is driven by a motor which produces a constant driving force. The vehicle travels from rest along a straight horizontal road. Friction and air resistance are negligible.

Which statement describes the variation with time of the power developed by the motor?

Which is a correct statement about mechanical power?

An electric motor lifts a load of weight W through a vertical height h in time t. The potential difference across the motor is V and the current through it is I.

What is the efficiency of the motor?

The engineer first investigates the emf and internal resistance of a solar cell under typical operating conditions.

The engineer determines how the potential difference across the solar cell varies with current. The results are shown in the graph in Figure 4.

The engineer uses the graph to deduce that when operating in typical conditions a single solar cell produces an emf of 0.70 V and has an internal resistance of

Explain how the engineer uses the graph to obtain the values for the emf and internal resistance of the solar cell.

To operate effectively the lamp in the road sign needs a minimum current of 75 mA. At this current the resistance of the filament lamp is 6.0 .

The engineer proposes to try the two circuits shown in Figure 5 and Figure 6.

Deduce, using calculations, whether the circuits in Figure 5 and Figure 6 are suitable for this application.

Solar cells convert solar energy to useful electrical energy in the road sign with an efficiency of 4.0%. The solar-cell supply used by the engineer has a total surface area of 32 cm².

Calculate the minimum intensity, in W m^–2, of the sunlight needed to provide the minimum current of 75 mA to the road sign when it has a resistance of 6.0 .