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A plot of potential energy and kinetic energy versus displacement x for a block attached to a spring obeying Hooke’s law is
  • a)
    a hyperbola
  • b)
    a straight line
  • c)
    an ellipse
  • d)
    a parabola
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A plot of potential energy and kinetic energy versus displacement x fo...
The graphs are parabolas as the potential and kinetic energy vary as x2.

 
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Most Upvoted Answer
A plot of potential energy and kinetic energy versus displacement x fo...
's Law can be described as follows:

1. At the equilibrium position (x = 0), the block is in its stable position with no displacement. Both the potential energy and kinetic energy are at their minimum values.

2. As the block is displaced from the equilibrium position in either direction, the potential energy starts to increase while the kinetic energy decreases. The potential energy curve is a symmetric parabolic shape, with the maximum potential energy occurring at the maximum displacement.

3. At the maximum displacement, the potential energy is at its maximum value, and the kinetic energy is at its minimum value. The block momentarily stops and changes direction, resulting in the spring trying to pull it back towards the equilibrium position.

4. As the block starts to move back towards the equilibrium position, the potential energy decreases while the kinetic energy increases. The potential energy curve follows the same symmetric parabolic shape as before.

5. When the block reaches the equilibrium position again, the potential energy is at its minimum value, and the kinetic energy is at its maximum value. The block is momentarily at its maximum speed before it starts to decelerate due to the spring's force.

6. The cycle repeats as the block continues to oscillate back and forth around the equilibrium position. The potential energy and kinetic energy interchange with each other, reaching their minimum and maximum values at the extremes of displacement.

Overall, the potential energy curve is a parabolic shape, while the kinetic energy curve is a mirror image of the potential energy curve. The total mechanical energy (sum of potential and kinetic energy) remains constant throughout the oscillation, indicating the conservation of energy.
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Community Answer
A plot of potential energy and kinetic energy versus displacement x fo...
D is correct.
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