Chapter 13 Equilibrium

1
Fundamentals of Physics Mechanics (Bilingual
Teaching) ???
School of Physical Science and Technology Yangtze
University
2
Chapter 8 Potential Energy and
Conservation of Energy

• 8-1 Potential Energy
• 8-2 Path Independence of Conservative
• Forces
• 8-3 Determining Potential Energy Values
• 8-4 Conservation of Mechanical Energy
• 8-5 Reading a Potential Energy Curve
• 8-6 Work Done on a System by an
• External Force
• 8-7 Conservation of Energy

3
8-1 Potential Energy

• Potential energy is energy that can be
• associated with the configuration of a
• system of objects that exert forces no one
• another.

4
8-1 Potential Energy

• Work and Potential Energy

Discuss the relation
Energy transferred from the tomato, Where does
it go? To Increase the
gravitational potential energy of the
tomato-earth system! (the seperation is increased
! )
Falling does , leads
Energy transferred from the gravitational
potential energy of the tomato-earth system to
the kinetic energy of the tomato !
5
8-1 Potential Energy

• Work and Potential Energy

This equation also applies to a block-spring
system
6
8-1 Potential Energy

• Conservative and Nonconservative Forces

• Key elements
• A system (two or more objects)
• 2. A force acts between a object and the rest
  part
• of the system
• when configuration changes, the force does
• work transffering the kinetic energy of
  the
• object into some other form of energy.
• Reversing the configuration changes, the force
• reverses the energy transfer, doing work
  .

7
8-1 Potential Energy

• Conservative and Nonconservative Forces
• Nonconservative Forces a force that is not
  
• 
  conservative
• Exp. (1) the kinetic frictional force (P 141)

A block is sliding on a rough surface, the
kinetic frictional force does negative work
Transfer kinetic energy thermal
energy So the thermal energy is not a potential
energy! The frictional force Nonconservative
Forces !
(2) the drag force
8
8-2 Path Independence of Conservative
Forces

• The closed-path test to determine whether
  a force is conservative or nonconservative.

9
8-2 Path Independence of Conservative
Forces
Prove Eq.(8-2), Sample Problem 8-1
b
b
1
1
2
2
a
a
If only a conservative force acts on the
particle, then
(8-2)
10
8-3 Determining Potential Energy Values
Find the relation between a conservative
force and the associated potential energy The
work done by a variable conservative force on a
particle (see Eq. 7-32)
(8-5)
(8-1)
(8-6)
Eq.(8-6) is the general relation we sought.
11
8-3 Determining Potential Energy Values
Gravitational potential energy A particle
is moving vertically along a y axis
(8-6)
From
(8-7)
(8-8)
(8-9)
12
8-3 Determining Potential Energy Values
Elastic potential energy A block-spring
system is vibrating, the spring force
does work on the block.
13
8-4 Conservation of Mechanical Energy
Mechanical energy THe Mechanical energy
of a system is the sum of its potential energy
and the kinetic energy of the objects within it

A conservative force does work on the
object changing the objects kinetic energy
(8-13)
The change in potential energy
(8-14)
14
8-4 Conservation of Mechanical Energy
( conservation of Mechanical energy )
In a isolated system where only
conservative forces cause energy changes, the
kinetic energy and potential energy can change,
but their sum, the mechanical energy of the
system, cannot change. The principle of
conservation of mechanical energy
15
8-4 Conservation of Mechanical Energy
(8-18)
When the mechanical energy of a system is
conserved we can relate the sum of kinetic
energy and potential energy at one instant to
that at another instant without considering the
intermediate motion and without finding the work
done by the forces involved.
16
8-4 Conservation of Mechanical Energy
A pendulum bob swings back and forth.
Sample Problem 8-4, Bungee jumping, P148
17

• Conservation of Mechanical Energy Bungee
  jumping at
• 
  Victoria Falls

18

• Victoria Falls (Zimbabwe- Zambia)

19
8-5 Reading a Potential Energy Curve
Finding the force Analytically
20
8-5 Reading a Potential Energy Curve

• is negative
• the slope of the
• curve

At ,
right
is a turning point
21
8-5 Reading a Potential Energy Curve
unstable equilibrium
neutral equilibrium
neutral equilibrium
K.E0
F0
stable equilibrium
22
8-6 Work Done on a System by an External
Force
Work is energy transferred to or from a system
by means of an external force acting on that
system.

23
8-6 Work Done on a System by an External
Force
No Friction Involved

throwing a ball upward, your applied force does
work
Earth
kinetic
potential
(8-23)
(8-24)
mechanical energy
( Work done on system, no friction involved )
24
8-6 Work Done on a System by an External
Force
Friction Involved
Block- Floor system
25
8-7 Conservation of Energy

• Countless experiments have proved

The total energy E of a system can change
only by amounts of energy that are transferred
to or from the system.
26
8-7 Conservation of Energy

• Isolated System

If a system is isolated from its environment No
energy transfers to or from it. W0
The total energy E of an isolated system cannot
change.
?
27
8-7 Conservation of Energy

• Isolated System

The total energy E of an isolated system cannot
change.
?
In an isolated system, we can relate the total
energy at one instant to the total energy at
another instant without considering the energies
at intermediate times.
?
This is a powerful tool in solving problems for
isolated system
28
8-7 Conservation of Energy

• Power

Power is the rate at which work is done by a
force. Power is the rate at which energy is
transferred by a force from one form to another.
?
?
average power
instantaneous power