Download Chapter 8a

Chapter 8: Potential Energy and
Conservation of Energy
Reading assignment: Chapter 8.5-8.6
Homework : due Friday, September 30, 2005
Problems:
40, 47, 65, 67, 73, 74
• Potential energy
• Conservative and non-conservative
forces
• CONSERVATION OF ENERGY
Review Important energy formulas:
Work:
 
W  F d
 F  d  cos 
xf
W   F  x dx
xi
 Fx  d x  Fy  d y  Fz  d z
Work done by spring:
Kinetic Energy:

1
Ws  k x 2f  xi2
2
1
2
K  mv
2
K   f k d

Potential energy U:
- Can be thought of as _________ energy that can
either do work or be converted to kinetic energy.
- When work gets done _____ an object, its
potential and/or kinetic energy ______________.
- There are different types of potential energy:
1. Gravitational energy
2. Elastic potential energy (energy in an stretched spring)
3. Others (magnetic, electric, chemical, …)
Gravitational
potential energy:
Ug  m g  y
-Potential energy only depends on y (height)
and not on x (lateral distance)
-MUST pick a point where potential energy is
considered zero!
U g  U f  U i  mg ( y f  yi )
Black board example 8.1
You are 1.80 m tall.
A 0.1 kg apple, which is hanging 1 m
above your head, drops on you.
What is the difference in
gravitational potential energy
when it hangs and when it hits
you?
1m
Elastic
potential energy:
Elastic potential energy stored in a spring:
1
2
U  k ( x  xeq )
2
Elastic potential energy depends on the distance from equilibrium
Conservation of mechanical energy
If we deal only with conservative forces and
If we deal with an isolated system (no energy added or removed):
The total mechanical energy of a system remains constant!!!!
E  K U
E… total energy
K… Kinetic energy
U… potential energy
The final and initial energy of a system remain the same:
Thus:
Remember:
Ki  U i  K f  U f
1
K  m  v2
2
Ei = Ef
Conservative and non-conservative forces
Conservative forces:
Work is independent of the _________ taken.
Work depends _______ on the final and initial point.
Work done is zero if the path is a __________ loop
(same beginning and ending points.)
We can
associate a potential energy with
conservative forces.
Work done by a conservative force:
Wc  U i  U f  U
Examples of conservative forces:
_____________________________________________
Conservative and non-conservative forces
Non-conservative forces:
A force is non-conservative if it causes a ______________ in
mechanical energy; mechanical energy is the sum of _________
and ____________ energy.
Example: Frictional force.
- This energy cannot be converted back into other forms of
energy (irreversible).
- Work does depend on path.
Sliding a book on a table
1
2
3
A child decides to go go down these 4 meter high (about 13 feet) slides
right after an ice storm. The presence of ice on the slide makes the
friction between the child and slide negligible. Which slide permits the
child to have the greatest change in potential energy?
1
3
2
4- None of the
above
Black board example 8.4
A frictionless roller coaster with an initial speed of vi = 10.00 m/s,
at the initial height h = 100.0 m, has a mass m = 1000.0 kg
(a) What is the speed at point A?
(b) What is the speed at point B
(c) How high will it move up on the last hill?
Work done by non-conservative forces
2. Situations involving kinetic friction.
(Friction is not a conservative force).
Kinetic friction is an example of a __________________ force.
If an object moves over a surface through a distance d, and it
experiences a kinetic frictional force of fk it is losing kinetic
energy
K friction  W friction   f k  d
Thus, the mechanical energy (E = U + K) of the
system is ________________ by this amount.
Black board example 8.7
A spring with a spring constant of 640 N/m is compressed 0.5 m. The
compressed spring accelerates a 3.5 kg block. After leaving the
spring at the spring’s relaxed length, the block travels over a
horizontal surface with a frictional coefficient mk = 0.25.
(a) Where does the block have maximum potential energy?
(b) Where does the block have maximum kinetic energy?
(c) How far along the rough horizontal surface does the block travel
until stopping?