So learning the concept of gravitational potential energy, my professor says that when lifting an object without any acceleration, the force we exert on the object to lift it is the same as the force of gravity pulling it down. For some reason my mind is having trouble understanding that.

If the force pushing up on it is the same as the force pushing down on it, then how can we be lifting the object?

I understand that we want it to have no velocity so that none of the energy is converted into kinetic energy and so that we only have potential energy and that's how we come up with $mgh$. I just don't understand how we are able to lift the object to give it the potential energy in the first place if the net force is zero?

  • $\begingroup$ @FrostyStraw: You wanna check this question if you are interested. $\endgroup$ – user36790 Oct 24 '14 at 5:29

There are two issues at play here.

If you lift something upward at constant speed, then the acceleration $\vec a$ is zero. This means that the net force $\vec F_\text{net}$ is zero by Newton's second law ($\vec{F}_\text{net}=m\vec{a}$). As long as something moves with constant velocity, all of the forces add up to zero (i.e., they cancel out). Yes, that is perhaps unintuitive, but it's part of the successful theory.

So let's say you believe that, or at least are willing to go along with that. There's still another subtlety that must be considered.

If initially the object is at rest with $v=0$ and you want to get it moving upward with constant speed, the upward force you exert must, for a very short time, be greater in magnitude than the gravitational force. This is needed in order to accelerate the object to a new velocity (again a consequence of $\vec F_\text{net}=m\vec a$). But once the desired upward velocity is attained, you reduce your upward force so that it's equal in magnitude to the gravitational force in order to keep the velocity constant.

Something similar happens for slowing the object back down to rest, except that your upward force has to be smaller than the gravitational force temporarily.


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