A-LevelPhysicsDynamics9702/22 · Feb/Mar 2019 · Q36 Marks

Two balls, X and Y, move along a horizontal frictionless surface, as illustrated in Fig. 3.1. Ball X has an initial velocity of 3.0ms⁻¹ in a direction along line AB. Ball Y has a mass of 2.5kg and an initial velocity of 9.6ms⁻¹ in a direction at an angle of 60° to line AB. The two balls collide at point B. The balls stick together and then travel along the horizontal surface in a direction at right-angles to the line AB, as shown in Fig. 3.2.

(a)By considering the components of momentum in the direction from A to B, show that ball X has a mass of 4.0 kg.[2]
(b)Calculate the common speed V of the two balls after the collision.[2]
(c)Determine the difference between the initial kinetic energy of ball X and the initial kinetic energy of ball Y.[2]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.

[1] (a) (m x 3.0) or (2.5 × 9.6 × cos 60°)
[1] (a) (m x 3.0) - (2.5 × 9.6 × cos 60°) = 0 so m = 4.0 (kg)
[1] (b) 2.5 x 9.6 x sin60° = (4.0 + 2.5) × V
[1] (b) V = 3.2 m s⁻¹
[1] (b) or use of momentum vector triangle: (4.0 × 3.0)² + [(4.0 + 2.5) × V]² = (2.5 × 9.6)²
[1] (b) V = 3.2 m s⁻¹
[1] (c) E = ½mv²
[1] (c) difference in Eᴋ = ½ × 2.5 × (9.6)² – ½ × 4.0 × (3.0)² = 97 J

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