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A box (400 kg) sits inside the trailer of a semitruck traveling at a speed of 25 m/s (~ 55 mph). Suddenly, a car in front of the truck stops in the road. The driver of the truck hits the brakes to bring the truck to a stop. Assume that the coefficient of static friction µs = 0.7 between the box and the floor of the trailer. Assume g = 10 m/s2. a) When the truck slows down while traveling left, what is the direction of the friction force on box 1 (right, left, none)? b) When the truck is slowing down, what is the maximum magnitude of the static friction force on box 1 (to slow it down with the truck and not let it slide)?  N c) When the truck is slowing down, what is the maximum magnitude of the truck’s acceleration such that box 1 does not slide?  m/s2

- October 5, 2022 - Edwin Tunner

A box (400 kg) sits inside the trailer of a semitruck traveling at a speed of 25 m/s (~ 55 mph). Suddenly, a car in front of the truck stops in the road. The driver of the truck hits the brakes to bring the truck to a stop. Assume that the coefficient of static friction µs = 0.7 between the box and the floor of the trailer. Assume g = 10 m/s2.

a) When the truck slows down while traveling left, what is the direction of the friction force on box 1 (right, left, none)?

b) When the truck is slowing down, what is the maximum magnitude of the static friction force on box 1 (to slow it down with the truck and not let it slide)?
 N

c) When the truck is slowing down, what is the maximum magnitude of the truck’s acceleration such that box 1 does not slide?
 m/s2

d) What is the minimum time for the truck to stop such that box 1 does not slide? Use your maximum acceleration from the previous problem. 
 s

e) Given this minimum time, what is the minimum distance for the truck to stop without box 1 sliding?
 m

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