Two ice-skaters and

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two ice-skaters

S_1

and

S_2

, initially at rest on a frictionless horizontal rink, push off against each other. During the interval

0\le t\le T

, the magnitude of the force on

S_1

due to

S_2

is given by

F(t)=F_0\,\sin\!\left(\dfrac{\pi t}{T}\right),

where

F_0=120\,\text{N}

and

T=0.40\,\text{s}

. After

t=T

the force is zero. The force on

S_2

is equal in magnitude and opposite in direction for the same time interval. The masses of

S_1

and

S_2

are

50\,\text{kg}

and

60\,\text{kg}

respectively. (a) Derive an expression for the magnitude of the impulse received by

S_1

in terms of

F_0

and

T

. (b) Hence calculate the numerical value of this impulse. (c) Determine the speeds acquired by both skaters immediately after they separate. (d) Compute the ratio of the kinetic energies of the two skaters after separation and interpret the result with reference to their masses.

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