Question

A Roman catapult relied on a heavy mass falling to the ground to launch a smaller mass into the air. If a mass of 200kg is allowed to fall 3m: What is the maximum energy the mass can have?
If the smaller mass rose 10m what is its mass?

Answer 1

This problem involves calculating the change in potential energy. The larger mass loses PE (it falls) and this energy is converted to the PE of the smaller mass. As a result, the smaller mass gains PE (it rises).

Answer 2

There is a mistake in your answer. To calculate the maximum energy you have to multipy your answer with g. Without this step the measurement unit becomes wrong:

J = (kg*m^2)/s^2

Your answer: kg*m

Apart from that mistake a good answer.

Answer 3

I made a careless mistake in the earlier answer. Here is the revised answer.

PE = mgh

PE (falling mass) = PE (mass being launched)
m(1)*g*h(1) = m(2)*g*h(2)
m(1)*h(1) = m(2)*h(2)

m(1) = 200 kg and m(2) = ?
h(1) = 3 m and h(2) = 10 m

(200 kg) (3 m) = (m) (10 m)
600 kg*m = (m) (10 m)
60 kg = m

PE = mgh = (600)(9.81) = 5886 J

The max energy is 5886 J.
The mass of the smaller object is 60 kg.

I don't know what I was thinking earlier. Sorry!

@guenny90: Thanks!