2-12. Crates A and B weigh and , respectively. The coefficient of kinetic friction between the ground and the crates follows a normal distribution . If the crates start from rest, determine the distribution of their speed after and the distribution of the force exerted by crate A on crate B during the motion.

Solution:

Free-Body Diagram: the free-body diagram of crates A and B are shown below.

Principle of Impulse and Momentum:

Crate A

The friction force acting on crate A

Then

Therefore

Crate B

The friction force acting on crate B

Then

Then we have

Thus,

Ans.

Ans.

From , we have

Thus,

Ans.

Ans.