A-LevelMathematicsMechanics9709/41 · Oct/Nov 2021 · Q25 Marks
Two small smooth spheres A and B, of equal radii and of masses km kg and m kg respectively, where k > 1, are free to move on a smooth horizontal plane. A is moving towards B with speed 6 m s⁻¹ and B is moving towards A with speed 2 m s⁻¹. After the collision A and B coalesce and move with speed 4 m s⁻¹.
- (a)Find k.[3]
- (b)Find, in terms of m, the loss of kinetic energy due to the collision.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] Attempt at use of conservation of momentum. 4 terms implied, i.e. m and km included before and after collision. Velocity after collision is the same for m and km.
- [A1] km×6 - m×2 = (km+m)×4
- [A1] k = 3
- [M1] Attempt at any of the three possible KE terms, unsimplified. k need not be substituted here. KE initial = ½×km×6² + ½×m×(-2)². KE after = ½×(km+m)×4².
- [A1 FT] Loss of KE = 24m J. FT on their k, KE loss =(10k-6)m, k > 0.6.
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