QUESTION: I have a question about work. Let's say that I'm lifting a 10kg object up 10 meters. W=Fd and F=ma so the work I would be doing is 10 x 9.8 x 10. That means that I applied 98N of force since 10 x 9.8. But gravity also applied 98N of force to that same object. Since the forces are equal and opposite, they cancel out so therefore no acceleration. And if there is no acceleration, that means there is no change in kinetic energy. And another definition of work is change of kinetic energy. But since there is no change in kinetic energy, that means no work. What am I doing wrong here? I am very confused.
ANSWER: In this case there is no change in KE. There's an increase in PE which equals mgh. So your work increased the PE by 980J.
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QUESTION: Thank you, but that is not what I asked. The work that I apply to the object is 980J. That means I applied 98N of force. Gravity also applies 98N of force. Gravity's force and my force are equal and opposite so they cancel each other out, so there is not net force. That means no acceleration. That means no change in KE. But defintion of work is change in KE. And since there's no change in KE, that means no work. But then just a while ago with the other formula of work which is W=Fd, I got that I did 980J of work. Why do these two ways contradict each other?
The definition of work does not have to mean a change in KE. If you do work pushing an object along a plane at a constant velocity and overcoming friction, that work shows up as heat and not a change in KE. In this case you did work to overcome gravity and raise an object.