Blocks and of masses and respectively are kept in contact on a smooth horizontal table

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

Problem

Blocks

X

and

Y

of masses

m

and

2m

respectively are kept in contact on a smooth horizontal table. A time-dependent horizontal force

F(t)=kt

(where

k

is a positive constant) starts acting on block

X

t=0

. The blocks start from rest and remain in contact throughout. (a) Show that the acceleration of the system at any instant

t

\dfrac{kt}{3m}

. (b) Hence find the magnitude of the force exerted by block

Y

on block

X

as a function of time. (c) Evaluate the force in part (b) at

t=4\,\text{s}

k=9\,\text{N}\,\text{s}^{-1}

and

m=1\,\text{kg}