6.22 - Summary
Work is the product of the force on an object and its displacement in the direction of
that force. It is a scalar quantity with units of joules (1 J = 1 kg·m^2 /s^2 ).
Work and several other scalar quantities can be computed by taking the dot product
of two vectors. The dot product is a scalar equal to the product of the magnitudes of
the two vectors and the cosine of the angle between them. Loosely, it tells you how
much of one vector is in the direction of another.
Energy is a property of an object or a system. It has units of joules and is a scalar
quantity. Energy can transfer between objects and change forms. Work on an object
or system will change its energy.
One form of energy is kinetic energy. It is the energy possessed by objects in
motion and is proportional to the object's mass and the square of its speed.
The work-kinetic energy theorem states that the work done on a particle or an object
modeled as a particle is equal to its change in kinetic energy. Positive work
increases the energy, while negative work decreases it.
Power is work divided by time. The unit of power is the watt (1 W = 1 J/s), a scalar
quantity. It is often expressed as a rate of energy consumption or output. For
example, a 100-watt light bulb converts 100 joules of electrical energy per second
into light and heat.
Another form of energy is potential energy. It is the energy related to the positions of the objects in a system and the forces between them.
Gravitational potential energy is an object's potential energy due to its position relative to a body such as the Earth.
Forces can be classified as conservative or non-conservative. An object acted upon only by conservative forces, such as gravitational and
spring forces, requires no net work to return to its original position. An object acted upon by non-conservative forces, such as kinetic friction,
will not return to its initial position without additional work being done on it.
When only conservative forces are present, the work to move an object between two points does not depend on the path taken. The work is
path independent. When non-conservative forces are acting, the work does depend on the path taken, and the work is path dependent.
The law of conservation of energy states that the total energy in an isolated system remains constant, though energy may change form or be
transferred from object to object within the system.
Mechanical energy is conserved only when there are no non-conservative forces acting in the system. When a non-conservative force such as
friction is present, the mechanical energy of the system decreases. The law of conservation of energy still holds, but we have not yet learned to
account for the other forms into which the mechanical energy might be transformed, such as thermal (heat) energy.