A-LevelPhysicsWork, energy and power9702/52 · Feb/Mar 2017 · Q115 Marks

A student is investigating the speed of a vehicle on a track when a small ball is projected into the vehicle, as shown in Fig. 1.1. ball vehicle track [Figure 1.1] The ball is projected towards the vehicle by a compressed spring. It is suggested that the relationship between the speed v of the vehicle and its mass M, after the ball embeds itself in the vehicle, is kx² = (M + b)v² where b is the mass of the ball, k is the spring constant and x is the compression of the spring. Design a laboratory experiment to test the relationship between v and M. Explain how your results could be used to plot a graph with 1/v² on the y-axis and to determine a value for k. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken.

A student is investigating the speed of a vehicle on a track when a small ball is projected into the vehicle, as shown in Fig. 1.1. ball vehicle track [Figure 1.1] The ball is projected towards the vehicle by a compressed spring. It is suggested that the relationship between the speed v of the vehicle and its mass M, after the ball embeds itself in the vehicle, is kx² = (M + b)v² where b is the mass of the ball, k is the spring constant and x is the compression of the spring. Design a laboratory experiment to test the relationship between v and M. Explain how your results could be used to plot a graph with 1/v² on the y-axis and to determine a value for k. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken.[15]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.

[1] M is the independent variable and v is the dependent variable, or vary M and measure v
[1] keep x/compression of spring constant
[1] labelled diagram including horizontal spring in line with vehicle attached to wall/retort stand
[1] use a ruler/calliper to determine compression of spring
[1] use of stopwatch/use of light gate connected to a timer/motion sensor correctly positioned
[1] use of balance to measure mass of vehicle M
[1] plots a graph of 1/v² against M
[1] relationship valid if a straight line produced
[1] k = 1 / gradient × x² or k = b / y - intercept × x²
[1] D1 use safety screen; use goggles to avoid ball/spring hitting eye
[1] D2 add masses to the vehicle to change M
[1] D3 repeat experiment for each M and average v
[1] D4 use of ruler to measure an appropriate distance for the time taken in stopwatch/light gate methods
[1] D5 method to determine speed of vehicle, e.g. time vehicle over a measured distance and use speed = distance/time
[1] D6 method to release ball with guide or support for spring /ball
[1] D7 release the ball close to the vehicle
[1] D8 detail on determining x e.g. difference between compressed length and original length
[1] D9 method to ensure constant speed along track, e.g. friction compensate track/use of air track
[1] D10 (relationship valid if a straight line produced) with (y-)intercept = b / kx²

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