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Spring 2004
PHY 2053C: College Physics A
Today: v Work and Energy ¸ Conserved quantities ¸ Work, Force and Displacement ¸ Kinetic and Potential Energy ¸ Conservation of Energy
n Motion, Forces, Energy, Heat, Waves n Dr. David M. Lind n Dr. Kun Yang n Dr. David Van Winkle
L8—Ch
Important Points from last Lecture
n Uniform circular motion implies presence of a “ Centripetal Force ” n This force can be delivered by friction , norma l, gravity or any other force you can think of. n Gravity is a general force between any objects with mass
n For orbital motion (planets, moon, satellites), gravity provides the centripetal force:
F G G
m 1 m 2
r
2
G
m 1 m 2
r
2 m^1
v^2
r
<=> G
m 2
2
r^3
T
2
Principle of Conserved
Quantities
n This week we will study Energy , n Next week we will study Momentum , both are conserved quantities: n In an isolated system , they can not be changed by any process, be it physical, chemical or biological. n Energy can be transformed between several different forms or transfered from one part of the system to another. n We will find that conserved quantities can simplify many of our calculations!
definition: Work
n Work is defined as force applied along a distance
n The unit of work is 1 Joule : 1J = 1 N.m = 1kg.m^2 /s^2
W F d F d cos
Work is done on the barbells!! -- F and d parallel
Example 1 : weightlifter
Force
distance
Work-Energy Principle
n Work can become several forms of energy. In this chapter, we will talk about: n Kinetic energy (energy of motion) n Gravitational potential energy
n Elastic potential energy (energy associated with position) Later (Chapter 14) we will see that: n Heat is also energy.
n Energy is “stored work” , which can be retrieved or changed from one form to another. n units : same as work -- Joule n The net work done on an object is equal to its change in kinetic energy.
n Assume a constant net force applied to a car over a distance d : What is the work done?
n We define as the “translational kinetic energy” of an object.
n Note that this is the net work on object: change in energy
Kinetic Energy
d Fnet
v 1 Fnet
v 2
from v 22 v 12 2 ad
⇒ W net F (^) net d mad m v^2
(^2) v 1
2 2 d d
W (^) net^12 mv 22 12 mv 12 KE 2 KE 1
KE^12 mv^2
F ma , with a v^2
(^2) v 12 2 d
Retrieving Kinetic Energy
n The hammer's kinetic energy KEh is used up as work on the nail : n As it strikes the nail, the nail exerts a force on the hammer, slowing it down with a constant force F
n from Action = -Reaction ,
n The work done on the nail is equal to KEH. Therefore all KE is used up as work on the nail.
W h F h d m
02 v 12
2 d
d
W h^1
m v 12 KE h
W (^) n F (^) n d F (^) h d KE (^) h
-F
Potential Energy: Gravitational
n Lift a brick of mass m from y 1 to y 2 What is the work done on the brick?
n But Wext can be retrieved: take the hand away and the brick will retrieve it as kinetic energy :
n Work had been stored by raising the brick's position: This form of energy is Gravitational Potential Energy
W ext F ext d mg h cos 0 m g h
FG= m g
Fext by hand
d = h
y 2
y 1
PE mgh
v^2 2 gh
=> KE^
m v^2
m 2 gh mgh
Potential Energy: Properties
n Potential Energy is an energy associated with
the position of an object.
Notes :
i) The gravitational PE depends on the height above a certain reference level. You may choose any point as the y = 0 point. But, be consistent! ii) Therefore, the value of PE is not unique even for a given position. But, ∆PE is the physically meaningful quantity and ∆PE does NOT depend on the choice of the reference level.
PE mg h (gravitational)
PE
1 2
k x
2 (elastic)
Conservation of Energy
n We just looked at an example, where potential energy of the brick is converted to kinetic energy as it falls
n For those and all points in-between, the total energy is constant:
Initially PE E P mg h
Finally KE E K^1
mv^2
E KE PE
2 mv
2
mgy const.
Question 3: Water Slides
Two water slides are shaped differently, but have the same length and start at the same height: Which rider is traveling faster at the bottom?
- Paul
- Kathleen
- Not enough information
- Both the same
Stay tuned...
n Friday: CAPA5/Recitation n Monday: Chapter 7 : Linear Momentum
Texts to evaluate!!! We would like everyone in the class to evaluate the quality of a potential new textbook. n We will give everyone who turns in an evaluation sheet on Monday comparing their chapter on “Work and Energy” the same extra credit points as a chapter summary. n There will also be a raffle of all those who turn in an evaluation sheet for the chance at a free DVD player.
S p e c i a l t r e a t :
