Friction problem of truck

  • #1
This problem seems like it's not too complicated but I am still getting confused:

A 30.0 kg packing case is initially at rest on the floor of a 1500-kg pickup truck. The coefficient of static friction between the case and the truck floor is 0.30 and the coefficient of kinetic friction is 0.20. Before each acceleration given below, the truck is traveling due north at constant speed. Find the magnitude and direction of the friction force acting on the case A) when the truck accelerates at 2.20 m/s^2 northward, and B) when it accelerates at 3.40 m/s^2 southward.

What I don't understand is how to use the coefficients of static/kinetic friction in this problem. I drew a free body diagram for the case and I found just 3 forces on the body: the weight of the case, the normal force, and friction. I'm not sure if it should be static or kinetic in either case A or B. For case A, I would think that since the truck is accelerating northward, the case would be "moving" southward relative to the truck (does that make sense?) so the friction force (static, kinetic?) should be poiting northward. Not sure how to get the magnitude of friction though, since just multiplying mu by the normal force does not give the right answer.
  • #2
When the truck and the case are moving with uniform velocity, there is no frictional force on the case. It is moving due to its inertia. Only two forces, the weight and the normal reaction, which balances each other, are acting on it.

Frictional forces come into play only when there is sliding or a tendency to slide between two surfaces. This happens only during acceleration. The truck accelerates, and the case wants to continue with its uniform velocity, and in this case there is the tendency for the case to slide wrt the truck.

If the acceleration is such that the frictional force is less than or equal to the maximum force of static friction, then the case will not slide; if it is more, then it will slide, and you will have to consider kinetic friction.

No you can try to do the math, and show us some work.

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