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?
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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