The classic introductory physics example for differentiating power from energy is two powerlifters lifting the same barbell to the same height, except one does it more quickly. The amount of gravitational potential energy given is the same, but done in different amounts of times and thus at different speeds. But i get confused because lifting the same barbell quicker requires a higher net force to be applied, which means the more powerful display of lifting required the muscles to output more force. And heat is also expended by the working muscles as well.
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I mean, sure? But who is contesting otherwise? If you are trying to argue that should be a tie-breaker in a weightlifting meet (for example), that’s just not how the rules of the game are written. If Steph Curry shoots a high-arcing shot, the ball travels a longer distance but it’s still worth the same 3 points.
Goes back to the basic Force = Mass * Acceleration equation. Mass is the same in both cases, but acceleration is larger/faster in the fast lifter, faster acceleration means more force.
Slow lifter: 1 mass * 1 speed = 1 force
Fast lifter: 1 mass * 2 speed = 2 force
Work is mass x displacement and doesn’t have the time element. So is energy which is why it doesn’t matter fast or slow.
I’m the box example, you are storing energy in the box. That energy potential is mass x gravity.
You’re not applying the higher force for the entire distance as you need to stop at some point to let the momentum settle.