Physics (AS & A Level) · Oct / Nov 2025 · Paper 51 · Question 1

On a bench, a steel ball of radius r is used to compress a spring by a distance x. The ball is held at rest in this position, as shown in Fig. 1.1. P compressed spring ball bench Fig. 1.1 The ball is released and rolls along the bench. At a fixed point P, the ball has speed v. The speed of the ball at P is determined using one light gate connected to a timer. Several steel balls of different radii are available. It is suggested that v is related to r by the relationship v 2 = Ykx2 r nρ where k is the spring constant of the spring, ρ is the density of the steel, and Y and n are constants. Plan a laboratory experiment to test the relationship between v and r. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for Y and n. In your plan you should include: • 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. 3 Diagram 4 [15]

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