A-LevelMathematicsMechanics9709/41 · May/June 2025 · Q57 Marks
When a particle P of mass mkg has speed ums⁻¹, its momentum is 4Ns and its kinetic energy is 16J.
- (a)Find the value of m and the value of u.[3]
- (b)P is now projected on a smooth horizontal surface with speed vms⁻¹ directly towards a particle Q of mass 1.25 kg which is stationary. After P and Q collide, the velocity of P is wms⁻¹ and the velocity of Q is 2wms⁻¹. The loss of kinetic energy in the collision is 25 J. Find the value of v and the value of w.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] ½mu² = 16
- [B1] mu = 4
- [B1] u=8,m=0.5
- [*M1] Using their value of m. Correct number of terms, allow sign errors. (0.5×v=0.5w+1.25×2w [v=6w])
- [*M1] Using their value of m (½×0.5×v² - (½×0.5×w² + ½×1.25×(2w)² )= ±25)
- [DM1] For equation in w or v only. Dependent on the two previous M marks (9w² - ½w² - 2.5w² - 25 = 0 [2w²=25])
- [A1] For both. Use of mg in momentum A0 (w = 2,v=12)
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