Question

A box of length 2m lies on the top of a rough wooden plank of length 10m. The coefficient of friction between the box and the plank is 0.1. The plank accelerates to the right at the rate of a=3m/s^2. If g=10m/s^2 then find the minimum time needed for the box to fall off the plank.

Answer 1

$$ma_b=ma_p-F_f=ma_p-\mu mg$$

$$a_b=a_p-\mu g=3-0.1(10)=2\frac{m}{s^2}$$

$$t=\sqrt{\frac{2(L-0.5l)}{a_b}}=\sqrt{\frac{2(10-0.5(2))}{2}}=3\ s$$