Question 1

What is the relationship between force and potential energy?

Accepted Answer

For a conservative force, the force is the negative gradient of potential energy: F = -∇U. It points in the direction in which potential energy decreases most rapidly, while the U(x) profile gives F_x = -dU/dx.

Question 2

Why is a bead constrained to a track different from a free particle?

Accepted Answer

A constrained bead can move only along the track, so its useful component is the tangential force F_s = -dU/ds. The constraint reaction prevents motion away from the allowed path; for curved motion, the normal components of the applied force and reaction together provide the required normal acceleration.

Question 3

What makes a force conservative?

Accepted Answer

A force is conservative when the work it does between two fixed positions is independent of the path followed. Equivalently, its net work around a closed loop is zero, and the work is W = -ΔU.

Question 4

How are stable and unstable equilibria identified on a potential-energy curve?

Accepted Answer

An equilibrium occurs where the slope is zero. A local minimum is stable because a small displacement produces a restoring force, while a local maximum is unstable because a small displacement drives the particle farther away.

Question 5

What is the potential energy of a spring?

Accepted Answer

For a spring of force constant k, with displacement x measured from equilibrium, the potential energy is U = 0.5 k x² and the restoring force is F = -kx. Changing the arbitrary zero of U does not change the force or energy differences.

Potential Energy Curve & Conservative Force Lab

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