Answer
(a) The mechanical advantage of the system is 2.
(b) The change in the gravitational potential energy of the weight is $1880~J$
(c) The work done is $1880~J$
(d) The person must pull the rope a distance of $8.00~m$
Work Step by Step
(a) Let $T$ be the tension in the rope. From the diagram, we can that that the force lifting the weight is $2T$. If a person exerts a force of $F$ on the rope, then the upward force exerted on the weight is $2F$. The mechanical advantage of the system is 2.
(b) We can find the change in the gravitational potential energy of the weight:
$\Delta U_g = mg~\Delta h = (48.0~kg)(9.80~m/s^2)(4.00~m) = 1880~J$
The change in the gravitational potential energy of the weight is $1880~J$
(c) The work that must be done is equal to the change in the gravitational potential energy of the weight, which is $1880~J$
(d) From the geometry of the system, we can see that when a person pulls the rope a distance $x$, the weight's height increases by $\frac{x}{2}$. Therefore, if the weight's height increases by $4.00~m$, the person must pull the rope a distance of $8.00~m$
