# Homework Help: Box on Cart (Friction)

1. Oct 16, 2005

### amcavoy

This is a link to a picture of my problem:

http://img57.imageshack.us/img57/9382/cart5rh.jpg [Broken]

It asks what tension on the rope would give the cart a maximum acceleration. The surface the cart is on is frictionless, while the cart itself is not (the surface the box is on).

To solve this, I figured that pulling the rope with a force of usN would give the maximum acceleration of the cart. However, this seems too easy; I think I may have not completely answered the question.

|T| = usN = usmg

Is my reasoning correct? Thanks.

Last edited by a moderator: May 2, 2017
2. Oct 16, 2005

### Staff: Mentor

Instead, think this way: What's the only force directly applied to the cart? What's the maximum acceleration acceleration that that force can give the cart? Use that to find the required tension in the rope.

3. Oct 16, 2005

### Staff: Mentor

What contact force is exerted on the cart?

4. Oct 16, 2005

### amcavoy

Ok this is what I came up with:

$$F_M=\mu_sN\implies a_M=\frac{\mu_sN}{M}$$

$$T=\left(M+m\right)a=\frac{\left(M+m\right)\mu_sN}{M};\quad N=mg$$

Is this correct?

Thanks again.

5. Oct 16, 2005

### Staff: Mentor

Now you've got it.

6. Oct 16, 2005

### amcavoy

Thanks Doc Al, I appreciate it.