PLEASE ANSWER USING THE 5 STEPS METHODPart II: A - K only
ll. BOUNCY BOUNCY BOUNCY BOUNCY... A perfect, massless spring with spring constant k : 30,000 N/m is afxed to a wall at the base of a ramp. A block (mass : 3kg) is touching the end of the spring that is away from the wall. The block begins at rest, and the spring begins at equilibrium (i.e. neither stretched nor compressed). A mysterious (yet somehow familiar seeming) stranger comes along and presses the block towards the wall, compressing the spring a distance of9cm. Then she releases it. 9 cm A. Calculate the work done by the spring as it returns to equilibrium. B. Calculate the kinetic energy ofthe block the moment the spring reaches equilibrium. Assume that friction is negligible. C. Calculate the height (d,) that the block will travel up the ramp before coming to rest. D. After coming to rest on the frictionless ramp, the block will of course begin to slide back down. Calculate the work done by gravity as the block slides back down. E. Calculate the kinetic energy of the block when it gets back to the bottom of the ramp. F. Naturally, the block will continue sliding (on the frictionless track) until it crashes back into the spring. Calculate the work the spring will have to do in order to stop the block. G. Calculate how far the spring will be compressed as it stops the block. Letters in diagrams refer to question parts (Problem 11, continued) So, the block will crash into the spring, compressing it a distance of9 cm (yep, that's what you should have gotten for G), before coming to rest. Then, of course, the spring will push the block back out (since, after all, it's a spring, and it always wants to return to equilibrium.) H. Calculate the work the spring will do on - J the block as it returns to equilibrium. 1. Calculate the KE of the block the moment the spring reaches equilibrium. J. Calculate the height the block will travel up the ramp before coming to rest. K. How long will this process continue? Describe what will happen over time. What you have discovered is that a spring force is a type of conservative force. L. Write down the definition ofa conservative force (from lecture) & explain how the work you did in parts A, B, E, F, G, H, and I shows that a spring force is a conservative force. We will now introduce a Mnew crincept'k'ri POTENTIAL ENERGY. Notice that, when the block is at the top of the ramp, gravity has done a bunch ofnegative work in order to bring the block to rest. It's now ready to do a bunch ofpm'itive work as the block travels back down. Similarly, when the spring is compressed 9 cm, the spring has done a bunch of negative work to stop the block and is now ready to do a bunch ofpm'itive work as it returns to equilibrium. In each case, the negative work on the trip against the force = the positive work on the way back, because both spring and gravity forces are conservative. Any time a conservative force does some negative work on an object, it then has the ability (the potential) to do the same amount ofpositive work as the object returns to its starting point. This positive work that the conservative force is ready to do is called POTENTIAL ENERGY, and it is represented by a capital letter U. So, potential energy is created when a conservative force does negative work, and potentially energy is used up when a conservative force does positive work. So, AU E the negative of the work that a conservative force has done; in other words, AU E the positive ofthe work that the conservative force is ready to do; (Notice that what we've actually dened is change in Potential Energy. We'll discuss this more in class, but for now you canjust ignore the deltas in the above definitions.)
