Chapter 6 Learning ObjectivesConcepts and Skills to Review
Gravitational forces (Section 2.5)
Newton's second law: force and acceleration (Section 3.4)
Falling objects (Section 3.6)
Components of vectors in two dimensions (Section 4.2)
Circular orbits (Section 5.4)
Summary
The principle of conservation of energy states that energy can be converted from one form to another, but the total energy in an isolated system never changes.
The work done by a constant force is
W = FΔr cos θ
(6-1)
where Δr is the displacement of the point of application of the force and θ is the angle between the force and displacement vectors.
The kinetic energy of an object of mass m moving with speed v is
Work done during a small displacement (variable forces) is
ΔW = FxΔx
(6-9)
The change in potential energy is equal to the negative of the work done by the conservative force that stores the potential energy
ΔU = -Wc
(6-14)
Why the minus sign? If the force does positive work, it takes energy from its stored potential energy and gives it away in some other form; therefore for a positive Wc , ΔU must be negative.
The elastic potential energy of an ideal spring of spring constant k and stretched or compressed a distance x from its relaxed length is
The gravitational potential energy for an object of mass m raised a distance h above some reference level near Earth's surface, where h is small relative to the radius of the Earth, is
U = mgh
(6-12)
if we choose U = 0 where h = 0.
The gravitational potential energy as a function of the distance between the two bodies of masses m1 and m2 whose centers are separated by a distance r is
The work done by a conservative force on an object does not depend on the path taken, but only on the initial and final positions of the object.
The principle of conservation of mechanical energy states that for a system on which only conservative forces act, the sum of the kinetic and potential energies is constant.
E = K + U
(6-15a)
ΔE = ΔK + ΔU = 0
(6-15b)
The work done on a point particle by nonconservative forces is equal to the change in the mechanical energy:
Wnc = ΔE =ΔK + ΔU
(6-16)
Average power is the average rate of energy transfer.
