Question

A man is standing on a platform that is connected to a pulley arrangement, as the drawing shows. By pulling upward on the rope with a force the man can raise the platform and himself. The total mass of the man plus the platform is 113 kg. What pulling force should the man apply to create an upward acceleration of 1.20 m/s2?

Answer 1

Answer:

The pulling force that the man should apply to create an upward acceleration of $1.20m/s^{2}$ is $P=621.5N$

Explanation:

Hi

As it shows in the drawing at the end, we have that the total mass of the man plus the platform is $113 kg$, then the force downward $W$ is $W=mg=113Kg*9.8m/s^{2}=1107.4N$.

Due the man needs to do a pulling force upward capable of lifting himself and the platform with an acceleration of $1.20m/s^{2}$, this force should create an acceleration greater than gravity by $1.20m/s^{2}$. then $a_{up}=g+1.2m/s^{2}=9.8m/s^{2}+1.2m/s^{2}=11m/s^{2}$. Therefore the force should be $P_{up}=ma_{up}=113kg*11m/s^{2}=1243N$.

Finally, as we have a pulley arrangement connected to the platform, it gives the man a mechanical advantage, so he has to do only half of that upward force

, therefore $P=\frac{1243N}{2}=621.5N$.