# Newton 2nd Law: Does vertical force (mass) affect the horizontal acceleration?

I learnt before that if 2 forces are perpendicular to each other, they should not affect each other. However in a recent experiment setup (asked in another question):

I believe the theoratical equation by newton 2nd law is

$$\begin{aligned} F_{horizontal} &= F_{vertical} \\ m_{cart}a_{cart} &= mg \\ a_{cart} &= \frac{mg}{m_{cart}} \\ \end{aligned}$$

Am I right so far? If so, this seem to imply that $m_{cart}$ (vertical force) is somehow affecting acceleration (horizontal)? Why is that?

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Assuming no friction? – ja72 Sep 27 '12 at 17:35

## 1 Answer

What the diagram doesn't show is the force on the pulley:

It's the vector sum of this force and the force due to the weight that gives a horizontal force on the cart.

The tension in the string must be constant, because if it varied along the string the string would strtech or contract until the tension was constant, so $F$ is the tension in the string times $\sqrt{2}$.

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hmm, I still don't get why forces acting perpendicular will affect each other? Does that have to do with the pulley? I know the tension in string is constant. For now, I think friction/mass of pulley is ignored ... not sure how `F=sqrt(2)`T? – Jiew Meng Sep 27 '12 at 9:49
try resolving the diagonal force into orthogonal components. – Nic Sep 27 '12 at 10:21
The pulley is exerting a force $F$ to the string. If you add (vector addition) the force $F$ to the downward force caused by the weight you'll find it's equal to the horizontal force on the cart. – John Rennie Sep 27 '12 at 10:26
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