Transcript Slide 1

Kinetic and Potential Energy
Potential Energy
An object can have potential energy by virtue of
its surroundings.
Familiar examples of potential energy:
• A wound-up spring
• A stretched elastic band
• An object at some height above the ground
Potential Energy
In raising a mass m to a height
h, the work done by the
external force is
W = F x cos(0) = Fx = mgh
We therefore define the
gravitational potential energy:
Concept Question
Is it possible for the
1) No.
gravitational potential
energy of an object to be
2) Yes.
negative?
3) Maybe.
Concept Question
Is it possible for the
1) No.
gravitational potential
energy of an object to be
2) Yes.
negative?
3) Maybe.
Gravitational PE is mgh, where height h is measured
relative to some arbitrary reference level where PE = 0.
For example, a book on a table has positive PE if the zero
reference level is chosen to be the floor. However, if the
ceiling is the zero level, then the book has negative PE on
the table. It is only differences (or changes) in PE that
have any physical meaning.
Potential Energy
This potential energy can become kinetic energy
if the object is dropped.
Potential energy is a property of a system as a
whole, not just of the object (because it depends
on external forces).
If
, where do we measure y from?
It turns out not to matter, as long as we are
consistent about where we choose y = 0. Only
changes in potential energy can be measured.
CHAPTER 11 # 44, 46, 48 & 50.
Concep Question 3
You and your friend both
solve a problem involving a
skier going down a slope,
starting from rest. The two of
you have chosen different
levels for y = 0 in this
problem. Which of the
following quantities will you
and your friend agree on?
A) skier’s PE
1) only B
2) only C
3) A, B, and C
4) only A and C
5) only B and C
B) skier’s change in PE
C) skier’s final KE
Concep Question 3
You and your friend both
solve a problem involving a
skier going down a slope,
starting from rest. The two of
you have chosen different
levels for y = 0 in this
problem. Which of the
following quantities will you
and your friend agree on?
A) skier’s PE
1) only B
2) only C
3) A, B, and C
4) only A and C
5) only B and C
B) skier’s change in PE
C) skier’s final KE
The gravitational PE depends upon the reference level,
but the difference ΔPE does not! The work done by
gravity must be the same in the two solutions, so ΔPE
and ΔKE should be the same.
Why Potential Energy is Useful
We can solve problems more easily than
with Newton’s Laws.
What is the speed of the
block when it reaches the
bottom of the incline?
v=0
h
θ
Energy approach:
v
Newton’s approach:
FN
max  mg sin   ax  g sin 
mgh = ½ mv2
mgx
v = √2gh
v 2  v0 2  2a x ( x  x 0 )
θ
mgy
mg
y
 0  2 g sin 
h

sin 
v 2  2 gh  v  2 gh
x
Why Potential Energy is Useful
We can also solve problems Newton’s
Laws can’t practically solve.
What is the speed of the
block when it reaches the
bottom of the incline?
v=0
h
v
Energy approach:
mgh = ½ mv2
v = √2gh
Newton’s approach:
I’ll accept this
answer…
Concept Question
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the
greater speed at the bottom of its ramp?
4) same speed
for all balls
1
2
3
Concept Question
Three balls of equal mass start from rest and roll down different
ramps. All ramps have the same height. Which ball has the
greater speed at the bottom of its ramp?
4) same speed
for all balls
1
2
3
All of the balls have the same initial gravitational PE, since they are
all at the same height (PE = mgh). Thus, when they get to the
bottom, they all have the same final KE, and hence the same speed
(KE = 1/2 mv2).
Follow-up: Which ball takes longest to get down the ramp?
Potential Energy
Potential energy can also be stored in a spring
when it is compressed; the figure below shows
potential energy yielding kinetic energy.
Potential Energy
The force required to
compress or stretch a
spring is:
(6-8)
where k is called the
spring constant, and
needs to be measured for
each spring.
The potential energy of a
spring is PE  1 k x 2 where
2
x  x1  xeq xeq = equilibrium
position
Applying Potential Energy to Problems
1. By how much does the gravitational potential
energy of a 64-kg pole vaulter change if her center
of mass rises about 4.0 m during the jump?
Applying Potential Energy to Problems
A 1.60-m tall person lifts a 2.10-kg book from the
ground so it is 2.20 m above the ground. What is
the potential energy of the book relative to (a) the
ground, and (b) the top of the person’s head? (c)
How is the work done by the person related to the
answers in parts (a) and (b)?
Applying Potential Energy to Problems
A 1.60-m tall person lifts a 2.10-kg book from the ground so it is 2.20 m
above the ground. What is the potential energy of the book relative to (a)
the ground, and (b) the top of the person’s head? (c) How is the work
done by the person related to the answers in parts (a) and (b)?
(a) Relative to the ground, the PE is given by

PEG  mg  ybook  yground    2.10 kg  9.80 m s 2
  2.20 m  
45.3 J
b) Relative to the top of the person’s head, the PE is given by

PEG  mg  ybook  yhead  h   2.10 kg  9.80 m s 2
  0.60 m   12 J
c) The work done by the person in lifting the book from the ground
to the final height is the same as the answer to part (a), 45.3 J.
In part (a), the PE is calculated relative to the starting location
of the application of the force on the book. The work done by
the person is not related to the answer to part (b).
Energy Ball Toss Lab
Energy Conservation
• Define
• Equation
Sample # 1
• Rock falling from cliff
Sample # 2
• Spring on table pushes object which falls
to ground. Find v at ground.
More fun problems
• CHAPTER 11 # 28, 31, 34, 55, 56, 59, 64,
65 & 66.