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326 Chapter 7 Conservation of Energy and an Introduction to Energy and Work

The work-energy theorem Work done on an object by the net force exerted on that object
for an object: The work-
energy theorem for an object W = K − K (7-9)
states that the net work done net f i
as an object moves through Kinetic energy of the object Kinetic energy of the object
a displacement—the sum after the work is done on it before the work is done on it
of the work done on the
object by individual forces
exerted on the object—is
equal to the change in the
object’s kinetic energy during
that displacement. This
theorem is valid whether the
path is curved or straight
and whether the forces are
constant or varying.

Work for a system: Work Work is the amount of energy transferred to the
is the amount of energy system by a force exerted on a point on the system Angle between the
transferred to the system by directions of
a force exerted on a point on W = Fd cos(q) F and d contact (7-11)
the system. The net work on a contact
system is equal to the sum of The magnitude of the The magnitude of the displacement
the work due to each external force exerted on a of the point of contact where the
force exerted on the system, point on the system force is exerted on the system in
which for each force is the the direction of the force.
magnitude of the external
force times the magnitude of
the displacement of the point
of contact of that force in the
direction of the force.
Work-energy theorem: Work Work is the amount of energy The change in energy of the
is the amount of energy transferred to the system by system (assuming work is the
transferred to the system by external forces only source of energy transfer) The change in all other
types of energy inside
external forces exerted on the system due to its
the system. If the system is con guration or the
not an object (the point of W = ∆E = ∆K + ∆U + ∆E internal internal motion of its
contact can move a different constituent parts
distance than the center The change in kinetic energy of the system, equal
of mass of the system) this to the product of the magnitude of the force F The change in potential (7-12)
work can go into more than exerted on the system and the magnitude of the energy of the system due
to reversible changes in
one type of energy. If there displacement of the center of mass of the system its con guration
in the direction of the force.
is no other source of energy
transfer, such as heating, then
the total change in energy
of the system is equal to the
work done on the system. If
the point of contact moves
a different distance than the
center of mass of the system
then energy can be converted
from one type to another
within the system, even if
the net work on the system
is zero.

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.

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