A-LevelMathematicsMechanics9709/41 · May/June 2023 · Q14 Marks

Two particles P and Q, of masses mkg and 0.3kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 5ms¯¹ directly towards Q. After P and Q collide, P moves with a speed of 2 ms¯¹ in the same direction as it was originally moving.

(a)Find, in terms of m, the speed of Q after the collision.[2]
(b)After this collision, Q moves directly towards a third particle R, of mass 0.6kg, which is at rest on the plane. Q is brought to rest in the collision with R, and R begins to move with a speed of 1.5 ms¯¹. Find the value of m.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[M1] Attempt at conservation of momentum; 3 non-zero terms (with m appearing in two terms); allow sign errors.
[A1] M1A0 if using g in momentum terms. v = -10m is A0.
[M1] Attempt at conservation of momentum between Q and R (so must be using correct masses of 0.3 and 0.6) to form a linear equation in m using their answer from (a); 2 non-zero terms; allow sign errors.
[A1FT] FT their +ve coefficient of m from (a) Condone including kg in answer.

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