Kinetic and Potential Energy

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Kinetic and Potential Energy
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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

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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
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Concept Question
Is it possible for the gravitational potential
energy of an object to be negative?

• 1) No.
• Yes.
• Maybe.

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Concept Question
Is it possible for the gravitational potential
energy of an object to be negative?

• 1) No.
• Yes.
• 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.
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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.
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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?

• 1) only B
• 2) only C
• 3) A, B, and C
• only A and C
• only B and C

A) skiers PE B) skiers change in PE
C) skiers final KE
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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?

• 1) only B
• 2) only C
• 3) A, B, and C
• only A and C
• only B and C

A) skiers PE B) skiers change in PE
C) skiers final KE
The gravitational PE depends upon the reference
level, but the difference ?PE does not! The
work done by gravity must be the same in the two
solutions, so ?PE and ?KE should be the same.
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Why Potential Energy is Useful
We can solve problems more easily than with
Newtons Laws.
What is the speed of the block when it reaches
the bottom of the incline?
v 0
h
?
v
Newtons approach
Energy approach
FN
mgh ½ mv2 v v2gh
mgx
?
mgy
mg
y
x
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Why Potential Energy is Useful
We can also solve problems Newtons Laws cant
practically solve.
What is the speed of the block when it reaches
the bottom of the incline?
v 0
h
v
Newtons approach
Energy approach
mgh ½ mv2 v v2gh
Ill accept this answer
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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
2
3
1
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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
3
1
2
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?
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Potential Energy
Potential energy can also be stored in a spring
when it is compressed the figure below shows
potential energy yielding kinetic energy.
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Potential Energy
The force required to compress or stretch a
spring is where k is called the spring
constant, and needs to be measured for each
spring.
(6-8)
The potential energy of a spring is
where
xeq equilibrium position
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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?

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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 persons
head? (c) How is the work done by the person
related to the answers in parts (a) and (b)?
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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 persons
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
b) Relative to the top of the persons head, the
PE is given by
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).
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Energy Ball Toss Lab
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Energy Conservation

• Define
• Equation

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Sample 1

• Rock falling from cliff

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Sample 2

• Spring on table pushes object which falls to
  ground. Find v at ground.

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More fun problems

• CHAPTER 11 28, 31, 34, 55, 56, 59, 64, 65 66.