# 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

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 $\sqrt{2}$.
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