Answer to Question #96740 in Physics for Singh

Question

(a) A flat-bed truck is driving east while speeding up. A box is resting in the centre of the bed of the truck. Nobody remembered to tie the box down so it is just sitting in the centre. The driver is speeding up gently so the box does not slip. Use towards the right on the page to represent east.
(b) The same flat-bed truck with the box in the back needs to stop suddenly. The driver slams on the brakes. The box slides towards the front of the bed of the truck.
(c) A conveyor belt is going full speed running to the right. A suitcase is dropped onto it. At the instant when the suitcase lands on the conveyor belt the suitcase is not yet travelling to the right, but the conveyor belt is going full speed. Draw the free body diagram for the moment just after the suitcase comes in contact with the conveyor belt, but has not started travelling to the right yet.

Answer 1

(a) If the truck accelerates and the box does not slip, it means that the truck's acceleration times mass of the box equals or less the force of static friction, or

$$ma\leq f_{\text{static}}.$$

(b) In this case the force of kinetic friction is smaller than the net force, and that net force is greater than the static friction:

$$ma\geq f_\text{static}\geq f_\text{kinetic}.$$

(c) Look at the figure below: