Example 3: Newton’s 2^nd law

The box B sits on the bed of a truck which is going around a turn of radius . At this instant the truck has a speed . If the coefficient of friction between B and the bed is , calculate the maximum rate at which the truck’s speed can increase without making the box slip.

Solution:

Slip condition,

Substitute (2) into (4), we get

Substitute (5) into (1) and (3), we get

Substitute (8) into (7), we get