a man is standing on a platform that is connected to a pulley arrangement, as the drawing shows. by pulling…

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?

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?

Answer

Explanation:

Step1: Apply Newton's second law

According to Newton's second law $F_{net}=ma$. The total upward force is $2P$ (since the rope pulls on the platform and the man with the same force $P$), and the total downward force is $mg$. So, $2P - mg=ma$.

Step2: Rearrange the formula to solve for $P$

First, factor out $m$ on the right - hand side: $2P=m(a + g)$. Then, solve for $P$: $P=\frac{m(a + g)}{2}$.

Step3: Substitute the given values

Given $m = 95.4$ kg, $a=1.20$ m/s², and $g = 9.8$ m/s². Substitute these values into the formula: $P=\frac{95.4\times(1.20 + 9.8)}{2}$. $P=\frac{95.4\times11}{2}=\frac{1049.4}{2}=524.7$ N

Answer:

$524.7$ N