Chapter 7: Kinetic Energy and
Work
Energy and Work
Kinetic energy
Work done by a constant force
Work–kinetic energy theorem
Work Done by a Gravitational Force
Work done by gravitational force
Tomato thrown upward
Lifting/lowering an object
Change in kinetic energy
Work Done by a Spring Force
Hooke’s law
Work done by a spring force
Work Done by a General
Variable Force
Work: variable force
 Calculus
 Divide area under curve
 Add increments of W (numerically)
Analytical form?
 Integration!!!
Sample Problem 7-8
Chapter 8: Potential Energy
and Conservation of Energy
Introduction
Potential Energy and Conservation of Energy
Conservative Forces
Gravitational and Elastic Potential Energy
Conservation of (Mechanical) Energy
Potential Energy Curve
External Forces
Work and Potential Energy
Potential Energy
General Form
Gravitational Potential Energy
Elastic Potential Energy
(Non-)Conservative Forces
 The system consists of two or more objects.
 A force acts between a particle–like object in the
system and the rest of the system.
 When the system configuration changes, the force does
work W1 on the particle–like object, transferring
energy between the kinetic energy K of the object and
some other form of energy of the system.
 When the configuration change is reversed, the force
reverses the energy transfer, doing work W2 in the
process.
 W1 = –W2  conservative force
Path Independence of Conservative
Forces
 The net work done by a conservative
force on a particle moving around
every closed path is zero.
 The work done by a conservative
force on a particle moving between
two points does not depend on the
path taken by the particle.
Sample Problem 8-1: A 2.0 kg block of cheese
that slides along a frictionless track from a to
point b. The cheese travels through a total
distance of 2.0 m, and a net vertical distance of
0.8 m. How much work is done on the cheese
by the gravitational force?
Conservation of Mechanical Energy
Mechanical Energy
Conservation of
Mechanical Energy
In an isolated system where
only conservative forces
cause energy changes, the
kinetic and potential energy
can change, but their sum,
the mechanical energy Emec
of the system, cannot change.
Potential Energy Curve
1D Motion
 Turning Points
 Equilibrium Points
– Neutral Equilibrium
– Unstable Equilibrium
– Stable Equilibrium
A plot of U(x), the potential energy function of a
system containing a particle confined to move
along the x axis. There is no friction, so
mechanical energy is conserved.
Conservation of Energy
Thermal Energy/Friction
 The total energy of a system
can change only by amounts
of energy that are transferred
to or from the system.
 The total energy E of an
isolated system cannot change.
Sample Problem 8-8