First slide

Friction

Question

A body of mass 40 kg resting on a rough horizontal surface is subjected to a force P which is just enough to start the motion of the body. If $μ_{s} = 0 .5$ , $μ_{k} = 0 .4$ , $g = 10 {ms}^{- 2}$ and the force P is continuously applied on the body, then the acceleration of the body is

Moderate

A

zero
B

1 ms^-2
C

2 ms^-2
D

2.4 ms^-2

Solution

Force, $P = f_{ms} = μ_{s} mg$ (when body is at rest)
When the body starts moving with acceleration a, then
$\begin{matrix} P - f_{k} = ma \\ μ_{s} mg - μ_{k} mg = ma \\ a = (μ_{s} - μ_{k}) g \\ a = (0 .5 - 0 .4) 10 \\ = 0 .1 \times 10 {ms}^{- 2} = 1 {ms}^{- 2} \end{matrix}$

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