Describing motion along a line

Questions 9 and 10 refer to the information below.

Regenerative braking supplies a current back to the power transmission system whilst slowing a vehicle. The arrangement shown can be used as a regenerative braking system on a train.

The coil rotates with the wheels of the train. Two copper rings are connected to the ends of the coil. The rings rotate with the coil and two carbon blocks make electrical contact with the rings as they rotate.

Describe how this arrangement can be used as a regenerative brake.

A specification for a new train states that the train should be able to accelerate to a speed of 360 km hour⁻¹ from rest, and that this acceleration should be completed within 40 km of level track.

The graph shows the performance of the train on a test run.

Calculate the acceleration of the train as it accelerates to a speed of

Deduce whether the performance of the train met the specification on this test run.

On curved tracks there is a maximum safe speed for the train.

Explain why there is a maximum safe speed for a train travelling on a curved track.

When the train travels at 200 km hour⁻¹, the minimum safe radius of curvature of the track is 1800 m.

Calculate the minimum safe radius of curvature for a speed of 360 km hour⁻¹.

The photograph shows a cyclist cycling at a constant velocity on horizontal ground.

The cyclist stops pedalling and comes to rest in a time of 5.2 s.

Sketch a graph to show how the cyclist’s velocity changes during this time.

Assume the deceleration is constant.

The cyclist travels 7.80 m while coming to rest.

Calculate the average resistive force on the cyclist and bicycle.

mass of cyclist and bicycle = 28.0 kg

A potential divider circuit may contain a component known as a potentiometer. One type of potentiometer consists of a track with terminals X and Y at either end. There is a sliding contact that can move along the track connected to a terminal Z as shown.

The length of the track is 115 mm and the width is 5.0 mm.

The resistance of the track between terminal X and terminal Y is 12.0 kΩ.

Calculate the thickness t of the track.

resistivity of track material = 0.49 Ω m

The potentiometer is used to monitor the displacement of a moving tool on a machine in a production line. The tool is attached to the sliding contact. The potentiometer is connected to a resistor of resistance R and a potential difference is applied as shown. The tool moves through a maximum displacement of 60 mm from end X, producing a maximum potential difference of 5.0 V between Z and X.

Show that the potential difference between X and Y is about 10 V.

Calculate the value of R.

When the circuit is assembled, using the correctly calculated resistance value and a battery of e.m.f. 12 V, it is found that the maximum output from the potentiometer is slightly less than 5.0 V.

Explain why the maximum output is slightly less than predicted.

The tool on the machine should not travel with a speed any larger than 0.8 m s⁻¹.

The graph shows how the displacement varies with time for the downward stroke of the moving tool.

Deduce whether this speed is exceeded by the moving tool.

A ball was dropped from rest, from a height above the ground. The ball bounced back up to about half its initial height.

Which graph shows how the velocity v of the ball varied with time t?

A physics class made a toy rocket. A drinks bottle was partially filled with water and inverted over a valve. An air pump delivered air to the bottle until the pressure forced the bottle from the valve and the water was ejected from the bottle at high speed.

A velocity-time graph for the bottle for the first 4 s after take-off is shown.

Determine the height to which the rocket travelled.

Sketch the corresponding acceleration-time graph on the axes below.

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.

A student investigates the motion of a friction‑free trolley down a ramp. On the top of the trolley there is a metal loop which makes contact with a length of thin resistance wire, AB, fixed above the ramp. The resistance wire has a uniform diameter.

The trolley accelerates down the ramp and the metal loop stays in contact with the wire along the full length of the ramp.

The student uses a protractor to measure the angle θ between the ramp and the horizontal

and records a value of 4° with an uncertainty of ±1°.

The two ends of the wire are connected to a 1.5 V cell. A data logger, set to measure potential difference, is connected to the metal loop and to the negative terminal of the cell.

Explain how the potential difference recorded by the data logger will vary as the loop moves along the length of the wire AB.

The graph shows the data obtained from the data logger.

Determine the velocity of the trolley at 1.5 s.

1.5 V represents a distance of 2.00 m.

The student calculated the velocity of the trolley at 2.0 s to be 1.5 m s^–1.

By considering the acceleration of the trolley, determine whether the student’s measurement of θ was within the uncertainty quoted.