Collisions

WME02Topic 2.43 questions

Newton's law of restitution, direct impact and successive collisions.

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Question 14 marks
A ball of mass $0.5\,\text{kg}$ moving on a smooth horizontal surface strikes a fixed smooth vertical wall at right angles with speed $8\,\text{m s}^{-1}$ . The coefficient of restitution between the ball and the wall is $0.75$ .

Find (a) the rebound speed, (b) the magnitude of the impulse exerted by the wall on the ball, and (c) the kinetic energy lost in the impact.
Mark scheme
- (a) Rebound speed $= 0.75 \times 8 = 6\,\text{m s}^{-1}$ (1)
- (b) M1 Impulse $= 0.5(6 - (-8))$ (1)
Question 26 marks
A smooth sphere $A$ of mass $2m$ moves with speed $3u$ on a smooth horizontal surface. It collides directly with a smooth sphere $B$ of mass $m$ , which is at rest. The spheres have equal radii and the coefficient of restitution between them is .

0.5(6−

(−8))

7\,\text{N s}

(1)

= \tfrac{1}{2}(0.5)(8^2 - 6^2) = 7\,\text{J}

(1)

\tfrac{1}{2}

\frac{1}{2}

(a) Find the speeds of $A$ and $B$ immediately after the collision.

(b) Find the kinetic energy lost in the collision, in terms of $m$ and $u$ .

Mark scheme

(a) M1 Conservation of momentum: $2m(3u) = 2mv_A + mv_B$ (1)
M1 Restitution: $v_B - v_A = \tfrac{1}{2}(3u)$ (1)
A1 $v_A = 1.5u$ (1)
A1 $v_B = 3u$ (1)
(b) M1 KE before $= 9mu^2$ ; KE after $= \tfrac{1}{2}(2m)(1.5u)^2 + \tfrac{1}{2}m(3u)^2 = 6.75mu^2$ (1)
A1 Loss $= \tfrac{9}{4}mu^2$ (1)

(

)

(

)

(

1.5

21m(3u)2=

6.75mu2