Potential Energy

Lecture 29 Friday November 14Chapter 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

• Work done by gravity

• Where did the energy you transferred go?

0cos cos 0

2.0*9.8*.925 18.1 JLIFTW Fd Fd mgd

0cos180 18.1 JGravW mgd

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.

0 ( )

or

g gf gi

g

g

E W Q

E K U U U W mg y

U mg y

U 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.

• Stretch spring from xi =0 to xf = x. The average force during this process of stretching is

SF kx

0 1

2 2 2f i

avg

F F kxF kx

Work done by us as we stretch spring is

21 1

2 2US avg avgW F d F x kx x kx

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 Conservation1. Define system2. Set Ei =Ef if system is isolated

Hoop Race

• Use energy conservation2 2

2 2

1 10

2 20

1 10

2 2

i f

i f

i i f f

K K Mv I

U Mgh U

K U K U

Mgh Mv I

R

v

22

2 2

2

1 1

2

2

Mgh M vR

Mghv a b

IM

R

Smallest I will be the fastest.

2

2

2

2

51

2

SPHERE

CYLINDER

HOOP

I MR

I MR

I MR

Power

• Power is the rate of transformation of energy

• Unit is 1 Watt=1W = 1 J/s• If energy being transformed is work, W then

EP

t

W F x xP F Fv

t t t

Is the work done by F + or - ?

Positive

negative

50%50%1. Positive2. negative

F

d

Is the work done by F + or - ?

Positive

negative

50%50%1. Positive2. negative

Fd

Is the work done by F + or - ?

Positive

negative

50%50%1. Positive2. negative

F

d

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

2

2

10 0

21

(1 cos )2

2 (1 cos ) 1.4 m/s

gi i gf fU K U K

mg y mv

mgL mv

v gL

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

• We want to find Kf .

Si i sf fU K U K

Problem 10:24

• Using the initial position as the compressed spring, final after book leaves spring:

2 2

2

1 11250 / (.04 )

2 20 0

1

2

Si i sf f

Si i

i Sf

f f

U K U K

U kx N m m

K U

K mv

Problem 10:24

• Finally

2 21250 N/m(.0400cm)

0.500kg

2.00 m/s

f i

kv x

m

Monday

• Oscillations• Read 14:1-3• Problems 10: 14,15,20,21,24,27,31,36,38,41,• 45