^Fig. 1^ Problem 3. A block is attached to a horizontal spring (Fig. 1). The oth
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Question
^Fig. 1^
Problem 3. A block is attached to a horizontal spring (Fig. 1). The other end of the spring is fixed. The equilibrium length of the spring is denoted as position 2. You compress the spring by hand to position 1, and then release it. The block eventually goes to some rightmost position 3 and starts oscillating. Consider only the motion from position 1 to 2 to 3. ignore energy losses.
(a) For each process (1 to 2, 2 to 3, and the entire 1 to 3) what are the changes in
kinetic energy and elastic potential energy - positive, negative or zero?
(b) Does the gravitational potential energy change?
(c) Is the displacement from equilibrium to the rightmost position equal to the dis-
placement from equilibrium to the leftmost position, in magnitude?
Explanation / Answer
a.
1-2: EPE is being converted into KE. KE is going from 0 to Positive, EPE is going from Positive to Zero.
2-3: At the neutral position, EPE is zero and KE is at it's maximum. Upon passing the neutral, KE begins to reduce as velocity goes down, and EPE gains magnitude in the <-- direction. At point 3, KE is zero and EPE is at it's maximum.
1-3: Kinetic Energy is 0 at both extremes of the range, EPE is at it's maximum magnitude in the --> direction at the beginning, and <-- at the end.
B. Since all movement is occurring in a direction perpendicular to the force of gravity, there is no change in GPE.
C. Yes. Since the distance between netural and the extremes is the same in both positions, the magnitude of energy stored in the spring is the same at both positions, albeit in opposing directions.
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