Question

A box rests on the (horizontal) back of a truck. The coefficient of static friction between the box and the surface on which it rests is 0.24. What maximum distance can the truck travel (starting from rest and moving horizontally with constant acceleration) in 3.0 s without having the box slide?

a) 19.6 m
b) 32.4 m
c) 41.5 m
d) 53.2 m

Answer 1

The maximum distance the truck can travel without having the box slide is approximately 32.4 m.

Step-by-step explanation:

Given that the coefficient of static friction between the box and the truck is 0.24, we can calculate the maximum force of static friction as fs = μs * N, where N is the normal force.

Since the truck is moving horizontally with constant acceleration, the normal force is equal to the weight of the box, which can be calculated as N = mg, where m is the mass of the box and g is the acceleration due to gravity.

The maximum distance the truck can travel without having the box slide can be determined using the equation x = 0.5 * a * t^2, where x is the distance, a is the acceleration of the truck, and t is the time.

Plugging in the values, we find that the maximum distance the truck can travel in 3.0 s without the box sliding is approximately 32.4 m.