CAIE A-Level Further Mathematics 3.6.1 Coefficient of Restitution

Practise applying Newton's restitution law to relative approach and separation speeds, then using momentum or the physical range of e to determine parameters.

Exam points

write separation speed over approach speed with a sign convention consistent with the impact line
combine the restitution equation with momentum to solve the coefficient or an unknown mass parameter
apply the interval from zero to one for e to convert its formula into a valid parameter range

[Maximum number: 2]

Find the value of e.

NEL: $v=e\left(u \cos 60^{\circ}+u \cos \theta\right)$

M1

$\begin{aligned} v=u, \quad u=e\left(\frac{1}{2} u+\frac{3}{4} u\right) e=\frac{4}{5} \end{aligned}$

A1

2

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3.6.1—Coefficient of restitution question 1