A man uses a pulley arrangement to lift a heavy crate.He applies a force that is one-fourth the weight of the crate, but moves the rope a distance four times the height that the create is lifted. Is the work done by the man greater than, equal to, or less than the work done by the rope on the crate? Explain.
work done by man: 4h*1/4 Weigh=wh work
work done on crate: weight*h=wh
To determine whether the work done by the man is greater than, equal to, or less than the work done by the rope on the crate, we need to consider the work done by both the man and the rope.
The work done on an object is calculated as the force applied multiplied by the distance over which the force is exerted. In this case:
- The force applied by the man is one-fourth the weight of the crate.
- The distance over which the force is exerted by the man is four times the height the crate is lifted.
Let's assume the weight of the crate is W. Therefore, the force applied by the man is 1/4 * W.
The work done by the man (W_man) is given by: W_man = Force * Distance = (1/4 * W) * (4 * height).
On the other hand, the work done by the rope on the crate (W_rope) is given by: W_rope = Force * Distance = (W) * (height).
To compare the two, we can simplify the equations:
W_man = (1/4 * W) * (4 * height) = W * (height) = W_rope.
From the calculations, we can see that the work done by the man (W_man) is equal to the work done by the rope on the crate (W_rope).
Therefore, the work done by the man is equal to the work done by the rope on the crate.