# Need help finding a strange vector system expression.

1. Oct 5, 2011

### Croix

1. The problem statement, all variables and given/known data
A toy cart of mass M1 moves on frictionless wheels as it is pulled by a string under tension T. A block of mass M2 rests on top of the cart. The coefficient of static friction between the block and cart is μ. The cart is moving up a ramp at angle θ. Find an expression for the maximum tension, T, that will not cause the block to slide off the cart.

No variables given, obviously, since I need to simplify an expression

2. Relevant equations

Fs = m μ
Weight = m g
I don't know any others, this is the problem.

3. The attempt at a solution
I know how to do the algebra to get an expression. I just don't know what formulas I can use to find the expression. I'm completely stumped. The entire setup with the cart is just odd to me, I've never seen anything like it. The tension in the string applies equally to the block on top of the cart yes? So I need to somehow find the maximum static friction force for the block?

2. Oct 5, 2011

### Staff: Mentor

As long as the block M2 is not slipping the tension pulling the cart M1 will produce the same acceleration in both.

Draw an FBD for M2. What conditions must be met for it to remain non-slipping?

3. Oct 5, 2011

### Croix

It has to have a net force of zero, yea?

4. Oct 5, 2011

### Staff: Mentor

M2 will be accelerating along with the cart, so no, the net force won't be zero. But a certain pair of forces has to sum to zero.

5. Oct 5, 2011

### Croix

The acceleration will equal the maximum static friction force.

6. Oct 5, 2011

### Staff: Mentor

Acceleration isn't a force, but you're starting to get the picture.

Keep in mind that acceleration isn't the only thing creating a force on the block. The cart is also traveling up a slope so gravity gets involved in the friction battle.