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Force from potential energy
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Force is the negative gradient of potential.
F = −dU/dxIn one dimension F = −dU/dx: the force points downhill on the potential curve, and its size is the slope. In 3-D, F = −∇U.
U = ½kx² gives F = −kx.
Mind the minus sign.
In more detail
For a conservative force, the force equals the negative gradient of the potential energy, F = −dU/dx. A steep slope in the potential energy means a strong force.
Real-world uses
- The electric field is the negative gradient of electric potential energy.
- Potential energy curves in molecules show the forces holding atoms together.
- Chemists model the bond between atoms as a potential energy well, and the force holding them together is the slope of that well.
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Frequently asked questions
What does the minus sign mean?
The force points towards lower potential energy, so objects tend to move downhill in potential energy.
Where is the force zero?
At points where the slope of the potential energy curve is zero, such as minima and maxima.
What does a steep potential energy curve mean?
A steep slope means a large force, so the system is strongly pushed back toward equilibrium.
Related topics in Work, Energy & Power
Elastic potential energy · Conservative forces · Non-conservative forces · Potential energy curves · Equilibrium types · Conservation of mechanical energy