Static frictions and moving boxes on top of a box

[okgo]

Homework Statement

http://www.screencast.com/users/trinhn812/folders/Jing/media/d77fab7d-ece6-4c9c-be65-bf41f94770fd

Homework Equations

I got the right answers doing the work shown, but I don't understand the logic of how I solved question 4.

The Attempt at a Solution

 

[tiny-tim]

hi okgo!

you need to use good ol' Newton's second law (F = ma) twice …

show us what you get ​

 

[okgo]

hmm so far..
m= mass of box and M=mass of cart. I assume the acceleration of the box and cart is the same.

F(box)=force(friction)=umg=ma
ug=a

F(cart)=force done by you=Ma
Substitute ug=a into the equation.
u*g*M=Force so mass of the box doesn't matter?

 

[tiny-tim]

F(cart)=force done by you=Ma

Is that for the cart M or for both M and m?

 

[okgo]

ohh I didn't include that. Thanks, it makes sense!