# Simple Dynamics Problem.

1. Mar 29, 2013

### Felafel

1. The problem statement, all variables and given/known data

I've solved it already, I think. I'm just not sure about the result.

There is a block (B), which is touching a cart (C) on one side.
Let an external force, parallel to the surface, $\vec{F_a}$ be applied on B

mass of B = m; mass of C = M; static friction coefficient between B and C = μ.

Taking no notice of the ground's friction, what is the minimum value of $\vec{F_a}$ such that the block doesn't fall?

3. The attempt at a solution

After drawing the free-body diagram for B, i see:
$\vec{F_s}$ (static friction force) $\leq m \cdot \vec{g}$
and being $\vec{F_s}=μ \cdot \vec{F_N}$ i get $\vec{F_N}= \frac{m \cdot \vec{g}}{μ}$
$\vec{F_a}=\vec{F_N} + \vec{F_f}$ the latter being the force applied to C, which makes it move.
$\vec{F_f}=\frac{\vec{F_N}}{M} * m$ . So,
$\vec{F_a}=\frac{m \cdot g}{μ}+ \frac{m^2 \cdot g}{μ \cdot M}$

is it okay?

2. Mar 29, 2013

### ehild

You made some little errors.

$\vec{F_s}$ (static friction force) $=-m \cdot \vec{g}$

${F_s}\leq \mu \cdot {F_N}$

The minimum value of Fa is the question. So $F_a\geq\frac{m \cdot g}{μ}+ \frac{m^2 \cdot g}{μ \cdot M}$

ehild

3. Mar 29, 2013

### vela

Staff Emeritus
Can you explain these two steps? I don't follow what you did here.

4. Mar 29, 2013

### haruspex

As vela notes, this is wrong. Try introducing an unknown for the acceleration of the system and developing the F=ma equation for each body separately.

5. Mar 30, 2013

### ehild

You meant by Ff the resultant force acting on B instead of C, didn't you?

haruspex: The OP solved the problem, but made some little errors when typing in. The result for the minimum applied force is correct, except the vector sign.

ehild