Acceleration

In an experiment to determine the acceleration of free‑fall, g, a metal cylinder was dropped from rest down a glass tube. A light gate was positioned close to the outside of the glass tube, as shown.

The light gate was connected to a data logger that recorded the time t taken for the cylinder to pass the gate.

A student recorded the following data.

The student omitted t₁ when calculating the mean time. He justified this by stating that t₁ is an anomalous result. Another student stated that the correct mean time should use all the data in the table.

Explain who is correct.

Calculate the percentage uncertainty in the mean time t_mean.

The student used the mean time to calculate the velocity of the metal cylinder as it moved past the light gate.

State the extra measurement the student must have made to calculate this velocity.

The metal cylinder fell through a distance 0.75 m before reaching the light gate.

Calculate the velocity of the metal cylinder as it reached the light gate.

Explain why a light gate and data logger were used in this experiment rather than a stopwatch. You should refer to your answer to (b)‌(i).

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.

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.