potential energy and inetic energy?
A wooden block with mass 1.65kg is placed against a compressed spring at the bottom of a slope inclined at an angle of 29.0∘ (point A). When the spring is released, it projects the block up the incline. At point B, a distance of 4.25m up the incline from A, the block is moving up the incline at a speed of 5.30m/s and is no longer in contact with the spring. The coefficient of kinetic friction between the block and incline is μk = 0.50. The mass of the spring is negligible.
Calculate the amount of potential energy that was initially stored in the spring.
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I uploaded the solution here: http://i.imgur.com/EXZaNgw.jpg
Potential Energy is what is classified as a state function. The only thing that matters is the final and initial positions, how it gets there (the path it takes, the speed it goes at, etc) does not matter. I see you added more info, think about it like this: You and your friend are both going to drop identical watermelons of the top of your house. You run it up the stairs and your friend casually walks up. When you are both holding the watermelons off the edge of the house, do they have different potential energies? Did you running it up transfer more energy into the melon? No, the melons are identical in mass, height (from the ground), and both are affected by the same force of gravity and therefore (per the equation of PE=(mass*height*gravity) they both have the same PE. The same thing applies in this question, how fast it makes it up makes no difference in the PE. Hope that clears it up.