Needed Energy For Lifting 200 kg weight

Question

1. I'd like to learn how much energy I need to lift a 200 kilograms weight on normal earth conditions?

2. For example how much electric power do we need?

I'm not a physicist and not a student and this is not my hw:) I just wondering.

Answer 1

In absence of a numerical value for that height, we shall call it $h$. Then, the energy necessary to lift $20 \textrm{ kg}$ at ‘normal earth conditions’ (namely $9.81 \frac{\textrm{N}}{\textrm{kg}}$ acceleration due to gravity), is given by

$$ E = m \times g \times h = 20 \textrm{ kg} \times 9.81 \frac{\textrm{N}}{\textrm{kg}} \times h $$

With your new height of fifty metres, we can then plug this into our equation and get

$$ E = 9810 J\quad.$$

This energy is independent of the speed at which you lift the mass (unless it has extra speed left over when reaching the height of $50 \textrm{ m}$).

Furthermore, we are able to directly compute the minimum force necessary to lift an item of $20 \textrm{ kg}$ against the earth’s gravitational field, namely $F_{\textrm{min}} = 196.2 \textrm{ N}$. A larger speed then requires a larger force to accelerate the mass to this speed.

Note that the above calculations assume Newtonian gravity, and, more importantly, a frictionless system. While the assumption of Newtonian gravity usually holds at the surface of the earth, I am looking forward to see a real world lifting device working without losses due to friction.