A flatbed truck carrying a heavy crate is travelling on a straight horizontal road at a speed of 20 m/s. The coefficient of static friction between the crate and the truck bed is 0.5 . What is the minimum stopping distance of the truck such that the crate does not slide forward on the truck bed during braking? (Take g = 10 m/s ^2 )

Step-by-step solution

Let the maximum deceleration of the truck without the crate sliding be a . In the frame of the decelerating truck, a pseudo force ma acts on the crate in the forward direction. To prevent sliding, this pseudo force must be balanced by the static friction force acting in the backward direction. The maximum static friction force available is f_ s, max = _s N = _s mg . Equating the pseudo force to the maximum static friction force: ma = _s mg a = _s g = 0.5 10 = 5 m/s ^2 The truck must decelerate at a maximum of 5 m/s