Hooke’s Law, Damping, and Elastic Potential Energy

All flashcards

Restoring force

A force directed toward equilibrium that opposes the displacement of a system.

Hooke’s law

The relationship $F=-kx$, where the restoring force is proportional to displacement and points in the opposite direction.

Force constant

The quantity $k$ that measures stiffness; a larger value means more force is needed for the same displacement.

Damping

The reduction in oscillation amplitude as dissipative forces transfer mechanical energy to other forms.

Elastic potential energy

Energy stored in a deformed system that can exert a restoring force.

Quiz questions

1. On a graph of applied force against displacement during gradual spring stretching, what does the work correspond to?Answer: The area beneath the force-versus-displacement curve.
2. What is the elastic potential energy of a Hooke’s-law system displaced by $x$?Answer: $PE_{el}=\frac{1}{2}kx^2$.
3. Why does the work required to stretch a Hooke’s-law spring gradually from equilibrium include a factor of $\frac{1}{2}$?Answer: The applied force rises uniformly from zero to its final value, so its average is half that value.
4. If all the stored spring energy becomes a projectile’s kinetic energy, which equation relates the energy to projectile speed?Answer: $PE_{el}=\frac{1}{2}mv^2$.
5. Why does a real toy gun generally transfer less spring energy to a projectile than an idealized model predicts?Answer: Friction, sound, and other losses divert some energy from the projectile.