First slide

Power

Question

A block of mass 20 kg is moved with constant velocity along an inclined plane of inclination 37° with help of a force of constant power 50 W. If the coefficient of kinetic friction between block and surface is 0.25, then what fraction of power is used against gravity?

Easy

A

$\frac{3}{4}$
B

$\frac{1}{4}$
C

$\frac{1}{2}$
D

$\frac{1}{8}$

Solution

$Power, P = Fv = (mgsin θ + μmgcos θ) v$
so, required fraction $= \frac{(mgsin θ) v}{(mgsin θ + μmgcos θ) v}$
$= \frac{\sin θ}{\sin θ + μcos θ} = \frac{3}{4}$

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