At which of the following positions does a spring have the least potential…
2023
At which of the following positions does a spring have the least potential energy?
- A.
The spring is neither compressed nor pulled out and is lying on the ground.
- B.
The spring is compressed to the minimum and is lying on the ground.
- C.
The spring is compressed to the minimum and is placed at a height.
- D.
The spring is pulled out to the maximum and is placed at a height.
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
A spring stores elastic potential energy U = ½k·x2, where x is the deformation measured from the spring's natural (unstretched, uncompressed) length. So U is smallest exactly when x = 0. A body also has gravitational potential energy U = mgh, which is least at the lowest height. Total stored potential energy is therefore least when there is no spring deformation AND the height is smallest.
Applying it here
Elastic part: with no compression and no stretch, the deformation is x = 0, so the elastic potential energy ½k·x2 becomes zero — its minimum possible value.
Gravitational part: resting on the ground means height h = 0, so mgh is also zero — the lowest gravitational potential energy.
Both contributions are simultaneously at their minimum, so the total potential energy is least.
Comparing the choices
Contrast with the other arrangements (each adds some stored energy):
Compressed a little on the ground: a non-zero deformation gives positive elastic energy ½k·x2 > 0, so it is not the least.
Compressed a little at a height: positive elastic energy plus positive gravitational energy mgh > 0 — more, not less.
Stretched to the maximum at a height: the largest deformation gives the largest elastic energy, plus gravitational energy from the height — the greatest, not the least.
Hence the position with no compression, no stretch, and resting on the ground holds the least potential energy.