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 143 kg. what pulling force should the man apply to create an upward acceleration of 1.20 m/s²?

Explanation:

Step1: Identify forces acting

The total mass $m = 143$ kg, acceleration $a=1.20$ m/s², and gravitational acceleration $g = 9.8$ m/s². The upward - acting forces are $2P$ (since the rope pulls the platform at two points) and the downward - acting force is $mg$. According to Newton's second law $F_{net}=ma$. So, $2P - mg=ma$.

Step2: Solve for pulling force $P$

First, rearrange the equation $2P - mg=ma$ to solve for $P$. Add $mg$ to both sides: $2P=ma + mg$. Factor out $m$: $2P=m(a + g)$. Then divide both sides by 2: $P=\frac{m(a + g)}{2}$.
Substitute $m = 143$ kg, $a = 1.20$ m/s², and $g = 9.8$ m/s² into the formula:
$P=\frac{143\times(1.20 + 9.8)}{2}=\frac{143\times11}{2}=\frac{1573}{2}=786.5$ N.

Answer:

$786.5$ N