Question

A block of $7\text{kg}$ is placed on a rough horizontal surface and is pulled through a variable force F(in N) = 5t, where 't' is time in second, at an angle of ${37}^{\circ }$ with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at t = 0 s. Find the time (in sec.) at which the block starts to slide. (Take $g=10{\text{m/s}}^2)$:

Answer 1

The block begins to slide if $Fcos{37}^{\circ }=\mu (mg-Fsin{37}^{\circ })$
$5t[\text{cos}{37}^{\circ }+\mu sin{37}^{\circ }]=\mu \text{mg}$
$5t[\frac{4}{5}+\frac{3}{5}]=70$ or t = 10 second