First slide

Power

Question

A body of mass m slides downward along a plane inclined at an angle $α$ . The coefficient of friction is $μ$ . The rate at which kinetic energy plus gravitational potential energy dissipates expressed as a function of time is

Moderate

A

$μ m t g^{2} \cos α$
B

$μ m t g^{2} \cos α (\sin α - μ \cos α)$
C

$μ m t g^{2} \sin α$
D

$μ m t g^{2} \sin α (\sin α - μ \cos α)$

Solution

The rate at which total mechanical energy dissipates with time is equal to the work done by the dissipative force per unit time.
$\begin{array}{l} \Rightarrow P_{d i s s i p a t i v e} = f V = f (a t) \\ \Rightarrow P_{d i s s i p a t i v e} = μ m t g \cos α (g (\sin α - μ \cos α)) \end{array}$

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