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 $vec{p}$ the man can raise the platform and himself. the total mass of the man plus the platform is 95.4 kg. what pulling force should the man apply to create an upward acceleration of 1.20 m/s²?

Explanation:

Step1: Apply Newton's second law

According to Newton's second law $F_{net}=ma$. The total upward force is $2P$ (two - rope segments pulling up), and the total downward force is $mg$. So, $2P - mg=ma$.

Step2: Rearrange the formula to solve for $P$

First, we can rewrite the equation $2P - mg=ma$ as $2P=ma + mg=m(a + g)$. Then $P=\frac{m(a + g)}{2}$.

Step3: Substitute the given values

We know that $m = 95.4$ kg, $a=1.20$ m/s², and $g = 9.8$ m/s². Substitute these values into the formula: $P=\frac{95.4\times(1.20 + 9.8)}{2}$.
Calculate the value inside the parentheses: $1.20+9.8 = 11$ m/s². Then $95.4\times11=1049.4$ N. Finally, $P=\frac{1049.4}{2}=524.7$ N.

Answer:

$524.7$ N