Potential Energy And Conservation Of Mass

Question 1

Conservative forces

Answer 1

A force is a conservative force if the net work it does on a particle moving around any closed path, from an initial point and then back to that point, is zero. Equivalently, a force is conservative if the net work it does on a particle moving between two points does not depend on the path taken by the par-ticle. The gravitational force and the spring force are conservative forces; the kinetic frictional force is a nonconservative force.

Question 2

Potential energy

Answer 2

A potential energy is energy that is associated with the configuration of a system in which a conservative force acts. When the conservative force does work W on a particle within the system, the change AU in the potential energy of the system is

ΔU = - W.

If the particle moves from point x; to point x,, the change in the potential energy of the system is

ΔU= - xf~xi F(x) dx

Question 3

Gravitational potential energy

Answer 3

The potential energy associated with a system consisting of Earth and a nearby particle is gravitational potential energy. If the particle moves from height
yi to height yf, the change in the gravitational potential energy of the particle-Earth system is

ΔU = mg(yf-yi) = mgΔy

If the reference point of the particle is set as yi = 0 and the corresponding gravitational potential energy of the system is set as
Ui = 0, then the gravitational potential energy U when the particle is at any height y is

U(y) = mgy.