Conservation & dissipation of energy

A toy car moves up a slope at a constant speed, as shown. The car is moved by a motor with a power output of 5.2 W. The car gains a gravitational potential energy of 0.40 J in a time of 1.1 s.

Which of the following expressions gives the work done, in J, against resistive forces?

*(a) Describe how the principle of energy conservation and the principle of momentum conservation apply to this situation.

Consider the situation from the instant the spring gun is released to the instant the bob reaches its maximum height.

When the modelling clay hits the pendulum bob, the pendulum swings to one side.

Show that the time taken for the pendulum bob to move from its lowest position to its highest position is about 0.6 s.

effective length of pendulum = 1.25 m

The pendulum bob was then attached to a spring of stiffness 0.12 N m^–1. When the bob was displaced vertically and released, it oscillated with a time period equal to that of the pendulum.

Calculate the mass of the pendulum bob.

Electric vehicles use a direct current (d.c.) electric motor powered by a battery for propulsion. A simplified diagram of a d.c. electric motor is shown.

A split ring consists of two semi‑circular sections that are attached to a coil. The coil is labelled ABCD. Two brushes, made of carbon, rub against and make electrical contact with the split ring.

*(a) Describe how this arrangement can lead to the coil rotating.

An advert for an electric car has the following information:

• electric motor can develop up to 390 kW output power

• car achieves a velocity of 28 m s^–1 from rest in 4.0 s at maximum power

Calculate the work done by resistive forces when the car accelerates to a velocity of

mass of car = 1950 kg

A website suggests that ‘fast‑charging’ the battery in an electric vehicle can increase the internal resistance of the battery.

Explain why an increase in internal resistance of a battery is a disadvantage.

A projectile of mass 65 g is fired vertically upwards into a stationary wooden block of mass 2.400 kg, as shown.

The projectile becomes embedded in the block. They both move vertically upwards through a vertical displacement of 55 cm before momentarily coming to rest.

Calculate the energy dissipated as the projectile hits the block.

Explain how the principle of conservation of energy applies to this collision.

Impact craters are formed when meteorites strike the surface of a planet. A student investigated some factors that might influence the formation of impact craters. He did this by dropping spheres of modelling clay into a tray of sand.

The diameter of the crater produced by each sphere was measured using vernier calipers as shown.

This process was repeated for spheres of different diameters.

In one test, the spheres were dropped from the same height.

Determine the factor by which the kinetic energy of the sphere just before impact increases when the sphere diameter is increased from 2.0 cm to 4.0 cm.

A ‘Gauss gun’ can be made from five ball bearings of equal mass and two magnets, as shown.

Pairs of ball bearings are placed to the right of two strong magnets. A single ball bearing is released from the left, as shown. The ball bearing is attracted to, and collides with, the first magnet. This and all subsequent collisions can be assumed to be elastic.

Explain what happens to make the last ball bearing on the right subsequently move off with a large velocity.

A student set up the apparatus shown to measure the speed of the last ball bearing. The ‘Gauss gun’ was placed at the end of a bench, so that the ball bearing left the gun and broke two strips of metal foil which formed part of an electric circuit.

As the ball bearing left the gun, it broke the first foil strip at its centre so that the capacitor started to discharge. When the ball bearing broke the second foil strip the capacitor discharge stopped.

Calculate the energy stored in the capacitor when it was fully charged.

The voltmeter reading halved in the time taken for the ball bearing to travel between the two foil strips.

Show that the time taken for the ball bearing to travel between the two foil strips was about 0.1 s.

The two foil strips were 0.50 m apart.

Calculate the horizontal velocity of the ball bearing.

The student positioned the second foil strip with its centre 8.0 cm lower than the centre of the first foil strip.

Deduce whether the ball bearing broke the second foil strip at its centre.

Assume the ball bearing was travelling horizontally as it broke the first foil strip.

A sports class is studying cycling. They produce a video of a cyclist on a horizontal lawn. The cyclist starts from rest. They produce a sketch graph of the velocity v of the cyclist against time t.

Explain the shape of this graph and include a consideration of force as part of your answer.

A student makes the following statement. The work done by the cyclist is converted into the kinetic energy of the cyclist and bicycle.

Criticise this statement.