ENERGY
WORK
• An object that has energy has the ability to
produce a change
•Work is how we transfer energy, it is equal to
the change in energy
•In order to do work on an object, you must
increase the energy within it
•Any type of energy can do work
Kinetic Energy
• Kinetic Energy (KE) is
the energy of motion
• More speed means more KE
Gravitational
Potential
Energy
• Potential
Energy is
Stored Energy
Heat Energy
• Heat is energy
that is created
by friction
• This could be
from sliding,
rubbing or
deformation
WORK
WORK EXAMPLES
•Let’s look at the following scenarios:
•Work or Not?
•Lifting a box above your head
work
•Holding that box there for 2 hours not work
•Sliding a box across a frictionless surface at
constant speed
not work
ENERGY EQUATIONS: WORK
•Work is the product of the force applied in the
direction of motion and the distance it is
applied
W = F(cosq )d
•When the force and the movement are
parallel, work is simply
Force (F)
W = Fd
θ
F||
ENERGY UNITS
•Notice: from the work formula, energy units
are a combo of Force (Newtons) and distance
(m) or Newton•meters (N•m)
•The SI units for energy are Joules (J).
•So, one Joule is equal to 1 Newton•meter.
1 J =1 N×m
POWER
•In physics, power just means the rate of doing
work
•So, faster work means more power
W
P=
t
•The units come out to Joules per second. J
•We call this a Watt (W) for short 1W = 1
s
Work Example
In the 1950s, an experimental train, which had a mass of
2.5 x 104 kg, was forced across a level track by a jet
engine that produced a thrust of 5.0 x 105 N for a
distance of 509 m. Find the work done on the train.
Equation:
Given:
m = 2.5´10 kg
5
Fengine = 5.0 ´10 N
4
d = 509m
Unknown:
W =?
W = Fd
Fengine
d = 509m
Fweight
m
= mg = m(9.8 2 )
s
Work Example
In the 1950s, an experimental train, which had a mass of
2.5 x 104 kg, was forced across a level track by a jet
engine that produced a thrust of 5.0 x 105 N for a
distance of 509 m. Find the work done on the train.
Equation:
Given:
m = 2.5´10 kg
5
Fengine = 5.0 ´10 N
4
d = 509m
Unknown:
W =?
W = Fd
= (5.0 ´10 N)(509m)
8
= 2.54 ´10 J
5
Fengine
d = 509m
Fweight
m
= mg = m(9.8 2 )
s
TIME TO PRACTICE!
Turn to pg. 409
Complete #5-11
If you finish early, try #2 on pg 408
KINETIC ENERGY
•Energy is the ability to do work
•Kinetic Energy (KE) is the energy of motion
•More speed means more KE
KINETIC ENERGY
ENERGY EQUATIONS: KINETIC E
•Let’s throw a block
•Work can transfer energy into the block
•Work is done while the block is being
accelerated by the hand a distance of d
ENERGY EQUATIONS: KINETIC E
•So, the work done is:
KE = Work = Fd= mad
•This time the force is simply ma
•Remember that acceleration equation?:
v = v + 2ad Þ ad =
2
f
2
i
v -v
2
f
2
2
i
ENERGY EQUATIONS: KINETIC E
•Let’s substitute:
KE = m×ad = m×
v -v
2
f
2
i
2
Þ KE = m(v - v )
2
f
1
2
2
i
•The normal equation assumes starting from
rest (vi = 0):
KE = mv
1
2
2
HW Q #1 pg 408
You will need to do some estimating for parts of this
problem. I am purposely leaving these a little vague.
Specify where you got information that you had to
look up or explain how you arrived at estimates for
mass and velocity.
a. Estimate the Kinetic Energy of a Chihuahua moving
as fast as it can.
POTENTIAL ENERGY
•Potential Energy is stored energy
•Gravitational Potential Energy (GPE) is when
energy is stored in an objects position (height)
•The higher an object goes, the more GPE
•(and the faster the speed it will have when it
hits the ground)
ELASTIC POTENTIAL ENERGY (EPE)
•The other type of Potential Energy we will look
at is Elastic Potential Energy (EPE)
•Instead of height, the energy is stored by
stretching an object.
•More stretching means more EPE
•ex. rubber band, spring
POTENTIAL ENERGY
ENERGY EQUATIONS: GPE
•For GPE, we still have force x distance, but
this time the force is the objects weight, mg
•This gives us the equation:
GPE = mgh
•We use h instead of d
since it will always be
height for GPE
F=mg
m
ENERGY EQUATIONS: ELASTIC PE
•EPE is trickier than GPE
•force changes depending on how much you
stretch the object
•This force depends on both the distance
stretched (x) and a spring constant (k)
Fs = kx
•This equation is known as Hooke’s Law
ENERGY EQUATIONS: ELASTIC PE
•This k comes from how much force is needed
to stretch a spring per a certain distance
•What is the k for this spring?
20
N
m
ENERGY EQUATIONS: ELASTIC PE
•Since the force at the beginning of the stretch
is different than the end, we use an average to
calculate the EPE:
æ Fsf + Fsi ö
EPE = Favg x = ç
÷x
è 2 ø
•Since we usually start the stretch from rest:
æ Fsf + 0 ö æ kx ö
EPE = ç
÷x = ç ÷x
è 2 ø è2ø
EPE = kx
1
2
2
ENERGY EQUATIONS: HEAT
•When pushing a block at constant speed
across a surface, the friction force is turned
into heat
f
•Since added force is only working against
friction (no a), all of the work done on the
block is then turned into heat
ENERGY EQUATIONS: HEAT
heat = work done
heat = f × d
•Remember that d is only during the friction
Proportionality Example
By what factor does the Kinetic Energy of a car
change if the speed doubles?
Given:
v = is doubled
Unknown:
1 2
KE = mv
2
how does KE change?
KEinital µ v
2
KE final µ(2v)
2
= 4v
4 KEinital = KE final
KE will be 4 times the original
2
Labette pg 479-481
Everyone should calculate their own
personal Power
(in other words, everyone should get some exercise)
There are 3 stations
1. Free Weights (Biceps)
2. Scales & Push ups (Triceps)
3. Stairs (legs)
Labette pg 479-481
You will need:
A
A
A
A
group composed of 2-3 people
stopwatch (use a cellphone)
meter stick
pencil & Your lab (duhhh!)
When you are done with data collection,
start your calculations
CONSERVATION OF ENERGY
•Energy cannot be created nor
destroyed, but only changed from
one form to another
•What does this mean?
CONSERVATION OF ENERGY
•All of the energy that you start with…
•you end with!
•initial energy = final energy
•Total energy at top
equals
•Total energy at bottom
•Total energy anywhere
CONSERVATION OF ENERGY
•All of the energy that you start with…
•you end with!
•initial energy = final energy
•Total energy at top
equals
•Total energy at bottom
•Total energy anywhere
CONSERVATION OF ENERGY
All GPE
GPE and KE
All KE
CONSERVATION OF ENERGY PROBLEMS
•Identify type of energy at beginning and end
•Full law in equation form:
KE i + GPE i + EPE i + work added = KE f + GPE f + EPE f + heat
•For most problems, many are zero
CONSERVATION OF ENERGY: EXAMPLE
•Rolling down a hill from rest
•Top (initial): all GPE
KE i + GPE i + EPE i + work added = KE f + GPE f + EPE f + heat
•Bottom (final): all KE
•Left with: GPE i = KE f
•or:
mgh = mv
1
2
2
gh = v
1
2
2
CONSERVATION OF ENERGY: EXAMPLE
A bow is used to shoot a .050 kg arrow into the air.
If the average force used to draw the bow is 110 N
and the bow is drawn 0.50 m, how fast is the arrow
moving when it has risen 35 meters above the bow?
(Assume air resistance is negligible)
Define:
What type of
energy is it?
initial : when bow is drawn (work)
and
final : when arrow is at 35 m (KE & GPE)
CONSERVATION OF ENERGY: EXAMPLE
Write out CoE eqn and cross out missing E’s
KE i + GPE i + EPE i + work added = KE f + GPE f + EPE f + heat
at rest
start at h = 0
finding through
work (no k)
moving
goes higher
nothing
stretched/pressed
no air resistance
CONSERVATION OF ENERGY: EXAMPLE
0.050 kg
kg arrow into the air.
•A bow is used to shoot a .050
110N
If the average force used to draw the bow is 110
N
and the bow is drawn 0.50
0.50 m,
m how fast is the arrow
35 meters
meters above
above the bow?
moving when it has risen 35
(Assume air resistance is negligible)
Givens:
m = 0.050 kg
F = 110N
d = 0.50 m
h = 35 m
Unknown
v = ? (speed in /s)
CONSERVATION OF ENERGY: EXAMPLE
rewrite and expand
work added = KE f + GPE f
Fd = mv + mgh solve for v
1
2
Fd - mgh = mv
1
2
2
2
2(Fd - mgh)
2(Fd - mgh)
2
=v Þ v =
m
m
CONSERVATION OF ENERGY: EXAMPLE
plug and chug
2(Fd - mgh)
v=
m
v=
[
(
2 (110N )(0.50m) - (.050kg) 9.8
v = 39
(.050kg)
m
s
m
s2
)( 35m)]
TIME TO PRACTICE IN PAIRS
Turn to pg. 495
If you finish early, start pg 496
KE i + GPE i + EPE i + work added = KE f + GPE f + EPE f + heat
KE i + GPE i + EPE i + work added = KE f + GPE f + EPE f + heat
KE i + GPE i + EPE i + work added = KE f + GPE f + EPE f + heat
KE i + GPE i + EPE i + work added = KE f + GPE f + EPE f + heat
Hopper Popper Lab
Strategy
1. Write down everything you could
measure with the resources you
haves
2. Write down your unknowns
Brain Break!
What’s wrong with Energy in this movie?
Discussion Question
A bowling ball attached to a wire is released one inch away
from someone’s face. It swings across the room, and then
back towards the person. It will…
a. Gain speed on the way back and hit the person in the face.
b. Stop one inch from the person’s face.
c. Lose speed and not make it all the way to the person’s
face.