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
WLIFT  Fd cos   Fd cos 00  mgd 
 2.0*9.8*.925  18.1 J
• Work done by gravity
WGrav  mgd cos180  18.1 J
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
2Mgh
I
M 2
R
Smallest I will be the fastest.
2
I SPHERE  MR 2
5
1
I CYLINDER  MR 2
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
tiv
ne
ga
Po
sit
i
d
ve
F
Is the work done by F + or - ?
1. Positive
2. negative
50%
50%
F
e
tiv
ne
ga
Po
sit
i
ve
d
Is the work done by F + or - ?
1. Positive
2. negative
50%
50%
e
tiv
ne
ga
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  K i  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  K i  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  K i  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