The Expression of Hurdle

Classical Mechanics Level 2

A small block of mass $m$ is kept on a rough inclined surface of inclination $\theta$ fixed in an elevator. The elevator start going up with a uniform velocity $v$ at $t=0$ and the block does not slide on the incline.

Find the work done by the friction force on the block in $t$ time.

mgvt cos^{2}\theta

mgvtsin(2\theta)

mgvt sin^{2}\theta

1 solution

Akshat Sharda
Jan 19, 2018

As the block goes up with a uniform velocity, the net force on the block is zero. So, balance forces along the incline to get, $|\vec{f}|=mg\sin\theta$ . Displacement $(\vec{s})$ will be $vt$ in $t$ time. Also, note that angle between friction force and displacement is $90°-\theta$ .

Therefore,

$W_{f}=\vec{f}.\vec{s}=(mg\sin\theta)(vt)\cos(90°-\theta)=mgvt\sin^{2}\theta$

The Expression of Hurdle

1 solution

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