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A horizontal force just sufficient to move a body of mass $4 \mathrm{~kg}$ lying on a rough horizontal surface, is applied on it. Coefficients of static and kinetic frictions are 0.8 and 0.6 respectively. If the force continues to act even after the body has started moving, the acceleration of the body is $\left(\right.$ take, $g=10 \mathrm{~ms}^{-2}$ ).
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Verified Answer
The correct answer is:
$2 ms^{-2}$
Initially
$\begin{aligned} & F=f_s=\mu_s N \\ & =0.4 \times 4 \times 10=32 \mathrm{~N}\end{aligned}$
Finally,
$\begin{aligned} & \mathrm{F}-\mathrm{f}_{\mathrm{k}}=\mathrm{ma} \\ & 32-\mu_{\mathrm{k}} \mathrm{mg}=\mathrm{ma} \\ & \Rightarrow \quad 32-0.6 \times 40=4 \mathrm{a} \\ & \Rightarrow \quad 8=4 \mathrm{a} \\ & \Rightarrow \mathrm{a}=2 \mathrm{~m} / \mathrm{s}^2\end{aligned}$
$\begin{aligned} & F=f_s=\mu_s N \\ & =0.4 \times 4 \times 10=32 \mathrm{~N}\end{aligned}$
Finally,
$\begin{aligned} & \mathrm{F}-\mathrm{f}_{\mathrm{k}}=\mathrm{ma} \\ & 32-\mu_{\mathrm{k}} \mathrm{mg}=\mathrm{ma} \\ & \Rightarrow \quad 32-0.6 \times 40=4 \mathrm{a} \\ & \Rightarrow \quad 8=4 \mathrm{a} \\ & \Rightarrow \mathrm{a}=2 \mathrm{~m} / \mathrm{s}^2\end{aligned}$
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