Really need help in finding the acceleration for built boxes.

Really need help in finding the acceleration for "built" boxes.

Homework Statement

Small block 1 with mass m = 2.56 kg sits on top of large block 2 of mass M = 7.7 kg, and the pair sit on a frictionless, horizontal table. Between the blocks: the coefficient of kinetic friction is μk = 0.146, and the coefficient of static friction is μs = 0.203.

Now, suppose the force applied to block 1 has magnitude F = 22.6 N, which is greater than 6.79 N. Find the magnitude of the acceleration of each block.

→ magnitude of the acceleration of block 1 (top block)
→ magnitude of the acceleration of block 2 (bottom block)

Homework Equations

→F = ma.
→ΣF_up = ΣF_down
→ΣF_left = ΣF_right
→Newtons' Laws of Motion

The Attempt at a Solution

Drew the FBD [free body diagram] (see attachment) and can't seem find the way to approach the problem.

The Attempt at a Solution

Attachments

• FBD.JPG
12 KB · Views: 313

Hint:

First determine the force due to friction on the lower block from the upper block. Use this force to determine an acceleration for both blocks taken together.

Determine the difference between the above force and the given force stated in the problem. Use the difference to determine the acceleration of the small block relative to the large block.

Then determine the absolute acceleration of the small block.

Hint:

First determine the force due to friction on the lower block from the upper block. Use this force to determine an acceleration for both blocks taken together.

Determine the difference between the above force and the given force stated in the problem. Use the difference to determine the acceleration of the small block relative to the large block.

Then determine the absolute acceleration of the small block.

Sorry. I am kind of confused here. Are you referring to the net force of each block?

The small block can only exert a frictional force on the lower block. Since there is no friction between the lower block and table, you can determine the acceleration of both blocks using the kinetic coefficient to determine the force applied to the whole system. That defines the acceleration of the blocks assuming no relative motion.

But the force is considerably larger so there is additional force that can accelerate the small block relative to the larger block. Using that force, determine the acceleration of the small block relative to the large block. Then combine the accelerations to determine the absolute acceleration of the small block. You already have determined the acceleration of the large block from the calculation above.

You can check you answers by multiplying the acceleration of each block by its mass, summing them, and comparing to the 22.6N

The small block can only exert a frictional force on the lower block. Since there is no friction between the lower block and table, you can determine the acceleration of both blocks using the kinetic coefficient to determine the force applied to the whole system. That defines the acceleration of the blocks assuming no relative motion.

But the force is considerably larger so there is additional force that can accelerate the small block relative to the larger block. Using that force, determine the acceleration of the small block relative to the large block. Then combine the accelerations to determine the absolute acceleration of the small block. You already have determined the acceleration of the large block from the calculation above.

You can check you answers by multiplying the acceleration of each block by its mass, summing them, and comparing to the 22.6N

Then, this means the amount of force you make both blocks move is F = (M + m)a? Then, the frictional force would be µ_k * mg [the upper box]? Also, if you said that..

"Using that force, determine the acceleration of the small block relative to the large block"

Then, this means I need to use F = ma?

Nevermind. Thanks for the help! I actually found the procedure online, and it works!