Question

A truck accelerates up a ${10}^{\circ }$ incline with a crate of 100 kg. value of static coefficient of friction between the crate and the truck surface is 0.3. The maximum value of acceleration $in\frac{m}{s^2}$ of the truck such that crate does not slide down is

Answer 1

Crate will acquire max acceleration when $(fs{)}_{max}$ will be acting on crate by truck and at that condition accelerationof truck and crate will be same. Increasing acceleration of truck after that will cause slipping of crate of truck.
$\left[\right(f_s{)}_{max}{]}_{CT}=\mu N_{CT}$

$\left[\right(f_s{)}_{max}{]}_{CT}-mg\sin {10}^{\circ }=ma$
$\mu mg\cos {10}^{\circ }-mg\sin {10}^{\circ }=ma$
or $a=1.1948\frac{m}{s^2}$