A-LevelMathematicsMechanics9709/41 · Oct/Nov 2022 · Q25 Marks
Small smooth spheres A and B, of equal radii and of masses 6 kg and 2 kg respectively, lie on a smooth horizontal plane. Initially A is moving towards B with speed 5 m s⁻¹ and B is moving towards A with speed 3 m s⁻¹. After the spheres collide, both A and B move in the same direction and the difference in the speeds of the spheres is 2 m s⁻¹.
- Find the loss of kinetic energy of the system due to the collision.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [*M1] Use conservation of momentum 4 dimensionally correct terms. Allow sign errors, VA and VB must be different.
- [DM1] 6×5+2×(-3)=6vA+2vB Use vB = vA+2 or vA = vB-2 with their momentum equation and solve for vA or vB Allow vB = vA ±2 or vA = vB ± 2.
- [A1] vA = 2.5 or vB = 4.5
- [M1] Attempt at initial KE, or final KE, or change in KE for A, or change in KE for B Allow use or their vA and/or vB . Allow if 2 KE equations seen.
- [A1] Loss of KE = 45 J Allow -45 J. Allow if mgv used in momentum equation.
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