First slide

Work done by Diff type of forces

Question

A small block of mass m is kept on a rough inclined surface of inclination $θ$ fixed in an elevator. The elevator goes up with a uniform velocity v and the block does not slide on the wedge. The work done by the force of friction on the block in a time t will be

Moderate

A

zero
B

$m g v t \cos^{2} θ$
C

$m g v t \sin^{2} θ$
D

$\frac{1}{2} m g v t \sin 2 θ$

Solution

As block does not side, Hence, force of friction.
$f = m g \sin θ$
In time t, displacement, $s = ν t$
$∴ W_{f} = f \cdot s \cdot \cos (90 ° - θ)$ = $μ m g \sin θ . v t . \sin θ = μ m g v t \sin^{2} θ$

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