PHYSICS 1A

POTENTIAL ENERGY AND CONSERVATION OF ENERGY

Conservative Forces

A force is conservative if the total work done by the force on an object is zero after the system returns to its original configuration after any exertion. The work done by a conservative force on a particle moving between two fixed points does not depend on its path. Work done from A to B is negative work done from B to A

Potential Energy

Potential energy is energy that is associated with the configuration of a system (e.g. location of objects relative to each other). When the conservative force does work W on a particle within the system, the change U in the potential energy of the system is

U = Uf Ui = -W = -Fx - F(x) dx

For the gravitational force U = mgyFor the spring force U = kxf2 - kxi2

Friction and drag are nonconservative: thermal energy is not potential energy.

Conservation of Mechanical Energy

Mechanical energy is the sum of kinetic energy and potential energyEmec = K + UIn an isolated system where only conservative forces cause energy changes, Emec cannot change even though U and K may change Emec = 0

If an external force does work on the system, the change on mechanical energy is equal to work done Emec = W

Work done on a system by an external force

When a kinetic frictional force acts within the system, then the thermal energy Eth of the system changes. The work done on the system is then

W = Emec + EthThe change Eth is related to the magnitude fk of the frictional force and the magnitude d of the displacement caused by the external force by

Eth = fkd

Conservation of Energy

The total energy E of a system ( the sum of its mechanical energy and its internal energies, including thermal energy) can change only by amounts of energy that are transferred to or from a system. This experimental fact is known as the law of conservation of energy. If work W is done on a system, then

W = E = Emec + Eint + Eth

PowerThe power due to a force is a rate at which that force transfers energy. If an amount of energy is transferred by a force in an amount of time t, the average power is

avg = / t