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A spring with unstretched length L1 is hung vertically, with the top end fixed in place, as shown in Figure 1 above. A block of mass M is attached to the bottom of the spring, as shown in Figure 2, and the spring has length L2 greater than L1 when the block hangs at rest. The block is then pulled downward and held in place so that the spring is stretched to a length L3 greater than L2, as shown in Figure 3.
The student releases the block. Consider the time during which the block is moving upward toward its equilibrium position and the spring length is still longer than L2. Indicate whether the total mechanical energy is increasing, decreasing, or constant for each of the systems listed below and explain why.
(a) System 1: The block – energy E1
(b) System 2: The block and the spring energy – E2
(c) System 3: The block and the Earth energy – E3
The block is released at time t = 0. The length of the spring is shown in the graph above as a function of time. During which interval(s), if any, is the weight force acting on the block greater than the spring force acting on the block? Explain your reasoning.
When the block reaches its lowest point after oscillating several times, the student attaches a new block of mass m less than M to the block of mass M without exerting any noticeable force to the block of mass M or changing the energy stored in the spring at that instant. In a clear, coherent, paragraph-length response that may reference equations, explain how the graph of length vs. time will change and why.
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