Question

A body of mass $2\text{kg}$ is kept on a rough horizontal surface. It is subjected to a force of a) $\text{5 N}$ b) $\text{20 N}$.
Given ${\mu }_s=0.5$ and ${\mu }_k=0.4$. Taking $g=10{\text{m/s}}^2$, find the acceleration in each case.

• A. zero, zero
• B. zero, $5{\text{m/s}}^2$
• C. zero, $6{\text{m/s}}^2$
• D. $4{\text{m/s}}^2,6{\text{m/s}}^2,$

Answer 1

The correct option is C zero, $6{\text{m/s}}^2$

$N=2g=20N$, Hence $f_s={\mu }_{s}N=10N$

since applied force $F_a=\text{5 N}$ in case (a) is $5N<10N$, the body will be at rest

$F_b=\text{20 N}$ in case (b)
$f_k={\mu }_{k}N=8N$: since $F_b>f_k$ in the second case, the body will acceletate.
Hence $20-8=2a\Rightarrow a=6{\text{m/s}}^2$