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 the 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 force is $2F$ (two segments of the rope pulling up) and the downward - acting force is $mg$. According to Newton's second law $F_{net}=ma$.
$2F - mg=ma$

Step2: Solve for the pulling force $F$

First, rewrite the equation from Step 1 for $F$:
\[

$$\begin{align*} 2F&=ma + mg\\ 2F&=m(a + g)\\ F&=\frac{m(a + g)}{2} \end{align*}$$

\]
Substitute $m = 143$ kg, $a = 1.20$ m/s² and $g = 9.8$ m/s² into the formula:
\[

$$\begin{align*} F&=\frac{143\times(1.20 + 9.8)}{2}\\ &=\frac{143\times11}{2}\\ &=\frac{1573}{2}\\ & = 786.5\text{ N} \end{align*}$$

\]

Answer:

$786.5$ N