Work and Energy.

Work W done by a constant force of magnitude F on an object as it is displaced by a distance d. The angle between the directions of F and d is θ . Work is positive if the object is displaced in the direction of the force and negative if it is displaced against the force. The work is zero if the displacement is perpendicular to the direction of the force.

Kinetic energy K for a mass m traveling at a speed v.

Potential energy U is the energy that an object of mass m has by virtue of its position relative to the surface of the earth. That position is measured by the height h of the object relative to an arbitrary zero level.

Conservative forces • Gravitational force • Elastic spring force • Electric force Non-conservative forces • Frictional forces • Air resistance • Tension • Normal force • Propulsion of a motor

A force is conservative if either: • The work done by the force on an object moving from one point to another depends only on the initial and final positions and is independent of the particular path taken. • The net work done by the force on an object moving around any closed path is zero

The total mechanical energy of a system, remains constant as the object moves, provided that the net work done by external non-conservative forces (such as friction and air resistance) is zero.

The work due to non-conservative forces Wnc is equal to the change in kinetic energy ΔK plus the change in gravitational potential energy ΔU plus any changes in internal energy due to friction.

The energy inherent to a particle by nature of it having a mass.

Power P is defined as the rate at which work is done. It can also be expressed in terms of the force F being applied to the object traveling at a speed v. It is more correct to express this version of the relationship as P = Fvcosθ where θ is the angle between F and v. M