Solving Friction Problem for 30.0 kg Packing Case in a 1500 kg Pickup Truck

[Amar.alchemy]

Homework Statement

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' northward and (b) when it accelerates at 3.40 m/s' southward.

Homework Equations

Newton's second law,static friction force and kinetic friction force equations

The Attempt at a Solution

I came to know that in both cases (ie a and b) frictional force is in the direction of acceleration of truck. Kindly explain me this??

 

[LowlyPion]

The force on the package from acceleration of the truck is south (when the truck is going north). This is in the frame of reference of the truck bed. The mass of the object resists the motion of the truck. The truck is the one that's going north, and it of course wants the package to go with it. If there was no friction the package would stay where it is as the truck drives out from beneath. So the truck is going to be exerting a force in whatever direction it accelerates, in order that the package would go with it. And it does this through the friction. Hence the force from acceleration in the frame of reference of the truck on the package is counter to the direction of the truck and the force of friction that is counter to this force is necessarily in the direction of acceleration.

 

[Amar.alchemy]

Thanks LowlyPion :-)