Question

A 20-kg box rests on the flat floor of a truck. The coefficients of friction between the box and floor are μs = 0.15 and μk = 0.10. The truck stops at a stop sign and then starts to move, with an acceleration of 2.0 m/s².

a) If the box is 5.0 m from the rear of the truck when it starts, how much time elapses before it falls off the rear of the truck? 3.13 s
b) How far does the truck travel in this time?

Answer 1

The maximum distance the truck can travel without the box sliding can be calculated by finding the maximum static friction force and using it to determine the distance.

Step-by-step explanation:

To find the maximum distance the truck can travel without the box sliding, we need to determine the maximum static friction force and then use it to calculate the distance. The maximum static friction force can be found by multiplying the coefficient of static friction (0.24) by the weight of the box (20 kg multiplied by the acceleration due to gravity, 9.8 m/s²).

The equation to find the maximum distance is: distance = (1/2) * acceleration * time². Plugging in the values into the equation, we get: distance = (1/2) * 0.24 * 20 kg * 9.8 m/s² * (3.0 s)². Solving the equation gives us the maximum distance the truck can travel without the box sliding.