Potential Energy
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Transcript Potential Energy
Potential Energy
Lecture 29 Friday November 14
Chapter 10: 6-10
Quiz
• In lab, you lift a 2 kg mass from the floor and
put it on top of the lab bench which is 92.5 cm
high.
• A) How much work did you do?
• B) How much work did the gravitational force
do?
• C) Where did the energy go that you put in as
work?
Answers
• d = 0.925 m, FLIFT = mg
0
WLIFT Fd cos Fd cos 0 mgd
2.0*9.8*.925 18.1 J
• Work done by gravity
WGrav mgd cos180 18.1J
0
• Where did the energy you transferred go?
Gravitational Potential Energy
• Book and the earth are the system, but do not
form an isolated system because we are
reaching in through the walls of the box.
E W Q
E K U g 0 (U gf U gi ) W mg y
U g mg y
or U g mgy
Note that ΔU depends only upon Δy, not on the path
the object took moving from the floor to the bench
top. No dependence upon x.
Problem 10:1 During an etiquette class, you walk
slowly and steadily at 0.20 m/s for 2.5 m with a 0.75
kg book balanced on your head. How much work
does your head do on the book?
Elastic Potential Energy
• Force exerted by a spring depends on how far
it has been stretched. Not a constant force.
FS kx
• Stretch spring from xi =0 to xf = x. The average
force during this process of stretching is
Favg
Ff Fi
2
kx 0 1
kx
2
2
Work done by us as we stretch spring is
1 2
1
WUS Favg d Favg x kx x kx
2
2
Where does this energy go?
Stored in spring and we can get it back out.
Hence we call the energy stored in the spring
potential energy, US = ½kx2.
Using Energy Conservation
1. Define system
2. Set Ei =Ef if system is isolated
Hoop Race
• Use energy conservation
1
1
2
Ki 0
K f Mv I 2
2
2
U i Mgh U f 0
Ki U i K f U f
1
1
2
0 Mgh Mv I 2
2
2
R
v
1
1 2
Mgh M 2 v
2
R
v a b
2
2
2 Mgh
I
M 2
R
Smallest I will be the fastest.
2
I SPHERE MR 2
5
1
2
I CYLINDER MR
2
I HOOP MR 2
Power
• Power is the rate of transformation of energy
E
P
t
• Unit is 1 Watt=1W = 1 J/s
• If energy being transformed is work, W then
W F x
x
P
F
Fv
t
t
t
Is the work done by F + or - ?
1. Positive
2. negative
50%
50%
e
at
iv
ne
g
Po
sit
i
d
ve
F
Is the work done by F + or - ?
1. Positive
2. negative
50%
50%
F
e
at
iv
ne
g
Po
sit
i
ve
d
Is the work done by F + or - ?
1. Positive
2. negative
50%
50%
e
at
iv
ne
g
Po
sit
i
d
ve
F
Problem 10:20
• A pendulum is made by tying a 500g ball to a
75-cm-long string. The pendulum is pulled 300
to one side and then released.
• A) What is the ball’s speed at the lowest point
in its trajectory?
• B) To what angle does the pendulum swing on
the other side.
Problem 10:20
• Use energy conservation
300
L=0.75 m
Δy=L-Lcos 300
Problem 10:20 cont
• Set y=0 at lowest point of swing
U gi Ki U gf K f
1 2
mg y 0 0 mv
2
1 2
mgL(1 cos ) mv
2
v 2 gL(1 cos ) 1.4 m/s
Problem 10:24
• A student places her 500g physics textbook on
a frictionless table. She pushes the book
against a spring 4.00cm and then releases the
book. What is the book’s speed as it slides
away? The spring constant is k = 1250 N/m.
Problem 10:24
• Use energy conservation
U Si Ki U sf K f
• We want to find Kf .
Problem 10:24
• Using the initial position as the compressed
spring, final after book leaves spring:
U Si Ki U sf K f
1 2 1
2
U Si kxi 1250 N / m (.04m)
2
2
Ki 0
U Sf 0
1 2
K f mv f
2
Problem 10:24
• Finally
k 2
1250 N/m
2
vf
xi
(.0400cm)
m
0.500 kg
2.00 m/s
Monday
• Oscillations
• Read 14:1-3
• Problems 10: 14,15,20,21,24,27,31,36,38,41,
•
45