11.54.Model:Model the ice cube as a particle, the spring as an ideal that obeys Hooke’s law, and the law of conservation of energy. Visualize:Solve:(a)The normal force does no work and the slope is frictionless, so mechanical energy is conserved. We’ve drawn two separate axes: a vertical y-axis to measure potential energy and a tilted s-axis to measure distance along the slope. Both have the same origin which is at the point where the spring is not compressed. Thus, the two axes are related by sin .ysθ=Also, this choice of origin makes the elastic potential energy simply 21s02()Ukss=−=212.ksBecause energy is conserved, we can relate the initial point—with the spring compressed—to the final point where the ice cube is at maximum height. We do notneed to find the speed with which it leaves the spring. We have 2g2s21g1s122220111KU U KU Umvmgyksmvmgyks++=++It is important to note that at the final point, when the ice cube is at y2, the end of the spring is only at s0. The
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This note was uploaded on 12/10/2011 for the course PHYS 1211 taught by Professor Geller during the Fall '09 term at UGA.