How Long Does It Take for a Block to Slide Across Another with Applied Force?

[Nuha99]

Homework Statement

A block of mass m rests on the left edge of a block of length L and mass M. Coefficient of kinetic friction between m and M is u. There is no friction between the bottom block (M) and the floor. A constant horizontal force F is applied to mass m, setting it in motion. How long will it take the block m to make it to the right of the bigger block? How far does the block M move in the process? view attached file for diagram.

Homework Equations

F = u R
s = ut + 1/2 at^2

The Attempt at a Solution

Net forfard force on m is = F - fk = F - uR1 = F - umg

Newton's second law: a = (F - umg)/m

s = 0 + 1/2 a t^2

L = 1/2 a t^2

solve for t: =

It was given that L = 3 m, M= 8kg, m = 2kg , u = 0.300 and F = 10 N

t =1.7 s

answer given in the book for t = 2.13 s.

I am missing something. Can you point out what might be wrong? thank you.

 

[Fellow]

hi, in your calculations, you did not take into account that the big block M was also moving.
your answer would be correct if the big block M did not move.

you should find the acceleration of the big block M and then find the distance that the big block M moves for a given time t.
den L = (distance moved by small block - distance moved by big block) and then it will be solved..

 

[Nuha99]

Thanks. I tried that before. But now I understand that the force on the big block due to the first block is fk. Not fk - F. With that correction, and your suggestion, I am getting the answer given in the book.

I am not still clearly understanding the fact that we are looking at the the first block's motion with respect to the earth. The method of finding t, in my first posting was done by observing the motion of m, with respect to the big block. Why is it wrong? I have few more similar problems and I need to understand this to do them correctly. Thanks.

 

[Doc Al]

I am not still clearly understanding the fact that we are looking at the the first block's motion with respect to the earth. The method of finding t, in my first posting was done by observing the motion of m, with respect to the big block. Why is it wrong?

In your first post you found the time it takes for the small block to move L = 3 m with respect to the earth. But you need to find the time it takes to move 3 m with respect to the big block, not the earth.

One way of looking at it is to solve for the time it takes for the small block to move 3 m farther than the big block (with respect to the earth).