How Do Friction Forces Act on a Packing Case in a Moving Truck?

[DWill]

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.

 

[Shooting Star]

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.

 

[Moetasim]

I can help clarify the use of coefficients of static and kinetic friction in this problem. First, it is important to understand that friction is a force that opposes motion between two surfaces in contact. The coefficient of friction is a value that represents the strength of this force between two specific surfaces.

In this problem, the case and the truck floor are the two surfaces in contact. The coefficient of static friction, denoted by "mu," is the value that represents the maximum amount of friction that can exist between two surfaces without causing them to move relative to each other. The coefficient of kinetic friction, also denoted by "mu," is the value that represents the amount of friction that exists between two surfaces in motion relative to each other.

When solving for the magnitude and direction of the friction force in this problem, it is important to consider the type of motion that is occurring. In case A, the truck is accelerating northward while the case is at rest on the truck floor. This means that the case is not yet in motion relative to the truck, so the coefficient of static friction should be used. The friction force will act in the opposite direction of the truck's acceleration, which is southward. To find the magnitude of the friction force, you can use the equation F = mu * N, where N is the normal force (equal to the weight of the case in this scenario).

In case B, the truck is accelerating southward while the case is already in motion on the truck floor. This means that the case is now in motion relative to the truck, so the coefficient of kinetic friction should be used. The friction force will still act in the opposite direction of the truck's acceleration, which is northward. Again, you can use the equation F = mu * N to find the magnitude of the friction force.

In summary, the key to solving this problem is understanding the difference between static and kinetic friction and applying the appropriate coefficient based on the type of motion that is occurring. I hope this helps clarify the confusion and helps you solve the problem correctly.