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Why is there no work
A skateboarder goes down a half-pipe and comes of the other side at a height of 3m. To find the initial velocity, I am supposed to use conservation of energy and assume there is no work done, but there does seem to be work. Wouldn't both gravity and the halfpipe's normal force do work, or do they cancel each other out?
Customer support service by UserEcho
The gravitational force and the normal force, I would say, definitely cancel out at a specific point but that is not why there is no work. The reason they say this is because they do not want you to account for friction. As you may know Work is defined to be -F*Δx, where F is the force in a direction and Δx is the change of the object's magnitude of distance in the same direction as the force. However, since you are ignoring friction you do not need to account for frictional force (thus no work is necessary). Keep in mind that there is work going down the ramp from gravity but there is also equal and opposite work going up the ramp as well, therefore you do not need to worry about that either.