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ENERGY
Modeling Unit VII
Whiteboard the Lab Results:
Sketch the graph for your spring Identify the color of your spring Just the straight line (no points) Label each axis with their proper units
Write the equation for your spring Replace y and x with the actual variables from the graph Include units for the slope and y-intercept
Write down what you think each of the following represent slope the y –intercept represent about the spring. The Area between your line and the displacement (stretch)
axis
Warm-up Question
The equation for a spring is:FT = (25N/m) Δd + 2.5N
Determine the following:a)The tension force (FT ) required to stretch
the spring 0.50 m.b) The amount of mass you would need to
hang from the spring to stretch it 0.50m
Spring-Force Lab Results
40F (N)
Δd (m)
50
25
0.5 10
20
15
105
45
35
30
0 1.4
How much mass needs to be added to the red spring to stretch it approximately 0.50 m?
40F (N)
Δd (m)
50
25
0.5 10
20
15
105
45
3530
0
F = (25N/m) Δd + 2.5N
F = (25 N/m) (0.50 m) + 2.5N = 12.5 N +2.5N = 15.0 N
FT = 15.0 N = Fg = mass (10N/kg) mass = 0.150 kg =150 g
Hooke’s Law for Springs
“k” = spring constant (strength of spring)
Ideal springs have no preload (F0). Any amount of force on a spring causes it
to stretch.
NdmNF 5.2/25
dkF T
General Equation:
Effort to Stretch Spring
The energy to stretch a spring involves the combination of…1. The force of tension in the spring (FT)
2. The displacement or stretch of the spring (Δx)
How do we represent this force-stretch combination? … or the combination of two values in general?
Review: finding displacement (Δd) If you are moving your displacement
depends on 2 things…1. How fast you are traveling2. How much time you are traveling at that
speed We found this graphically by finding the
area under the curve of a velocity versus time graph.
Δd = (2m/s)•6s = 12m
Δd = (½)•bh =
9m
During Constant Velocity: During Acceleration:
40FT (N)
Δd (m)
50
25
0.5 10
20
15
105
45
35
30
0
Representing Effort to stretch a spring:
Effort to stretch spring = area under FT vs. stretch (Δd) graph
Effort =
Finding Effort Mathematically
dFbh T2
1
2
1
... since dkFT
ddknergy2
1E
Energy storedIn a Spring (Eel) =
Area underThe graph
2
2
1dkEel
The effort exerted to stretch a spring can be used to do things (launch a projectile, etc…)
We can say that ENERGY is stored in a stretched or compressed spring.
Energy Stored in a Spring (Eel)
2
2
1dkEel
mNmm
N 2 :Units JmN 11
Joules (J) are the standard units for ENERGY A calorie is also a unit of energy.
Eel = Elastic Energyk = Spring ConstantΔd = displacement or stretch
Money Analogy for Energy
Use a whiteboard to illustrate how money ($) is used and moves in our society:
Consider the following questions? How is $ moved or is transferred in society? What can you do with $? Where is $ stored when it is not being
transferred? How do individuals get $? Etc... Be creative! (school appropriate and
legal)
Important Ideas about Money $ is transferred between people You get $ by working $ gives you the ability to do things $ is stored in different places (banks,
pockets, etc…) The flow of money can be cyclic
Analogy for Energy Spring – our system, something that can
store energy. A spring is like a bank, a place where $ can be
stored. Energy – gives you the ability to do things /
change things. Energy is like $, which gives you the ability to
do things in society. It cannot be created or destroyed, just
transferred from one place to another. “Working” – transferring energy from one
system to another. Working = transferring $ from one person to
another(losing and gaining $)
Energy ($) Storage Accounts Elastic Energy Account (Eel)– you can store
energy in an elastic material by working on it (apply a force over some displacement)
Gravitational Energy Account (Eg) – you can store energy in the Earth’s gravitational field by increasing the distance between the earth and an object.
Kinetic Energy Account (Ek) – the energy stored in moving objects.
Internal Energy Account (Eint) – the energy stored in the random motion of atoms in a system. Measured by change in temperatures.
Energy Bar Charts (LOL)
A visual way to account for the energy in a system. Where the energy is being stored and any transfers, into or out of the system (bank)
Worksheet 3a (Problem #1) v1
Initial
Final Define the system
as… Spring + Cart + Earth
NO FRICTION
Spring+ Cart + Earth
Worksheet 3a (Problem #1) v2
Initial
Final Define the system
as… Spring + Cart + Earth
WITH FRICTION
Spring+ Cart + Earth
Worksheet 3a (Problem #1) v3
Initial
Final Define the system
as… Cart + Earth NO FRICTION
Cart +
Earth
+ work is doneon the cart by
the spring
Worksheet 3a (Problem #1) v4
Initial
Final Define the system
as… the Spring NO FRICTION
Spring
- Work is doneon the spring by
the cart
Kinetic Energy Account:
What visually tells us that an object has more or less kinetic energy (Ek)? Its velocity or speed
…so the kinetic energy an object has depends on its velocity.
Studying Kinetic Energy (Ek & V)
If we pull the cart back, what kind of energy is stored in the system?
Where does the energy go when you release the car and the spring has lost all its stored energy?
Motion Sensor
m = 0.291kg
Δx
2
2
1xkEel kE
Ek (J)
V(m/s)
?0
0
Ek(J) V(m/s)
mNJ
ss
mkgN
The energy stored in moving objects. Depends on the mass and velocity of an object. Kinetic energy increases as mass increases. Kinetic energy increases when velocity increases.
2
2
1mVEk
Energy Review
What is energy? The ability to do something Gained or lost through “working” (W=FΔx)
How or where can energy be stored? In a stretched spring or elastic material
(Eel = 1/2k(Δx)2) In a moving object (Ek = 1/2mV2) By raising an object off the ground (Eg =?)
In the motion of atoms or molecules (Eint)
Gravitational Energy (Eg) Account To be above the
ground something has to do work ON the car to give it some Eg:
Fg = mg
F =_____
h
Eg = g = 10N/kg
Whiteboard Problem
How high should the cart be placed so that it will have a velocity of 1m/s when it goes through the photogate?
(Photogate)
h = ?h = 0m
m = 0.291kg
Solving Other Problems Changing gravitational energy to kinetic
energy is useful for solving many different types of problems.
Straight Ramps
1
Curved Ramps
11
2
FreefallPendulums
2 2
1
2
h
The speeds will be the same, but the directions different!
WK3a Problem #2
What is the car’s velocity halfway up the loop?
Initial
Final
m = 500kgk = 8000N/mΔx = 5mh = 0m
h = 10mV = ?
20m
CartSpringEarth
WK3a Problem #8
How much force did Super Man use when stopping the train?
m = 100,000kgV = 22.7m/s or 50mi/hr
Δx = 50mV = 0m/sF = ?
Initial: Final:
TrainSuperman
Whiteboard Problem You are driving along at 22.7m/s
(50mph) on a wet country road late at night when a deer jumps out 20m in front of your car. If you immediately slam on your breaks how fast will you be going when you hit the deer? The car’s mass is 1500kg and the coefficient of kinetic friction is 0.6
WK3b Answers #1 & 2
1. Δx = 2m
2. V = 9.5m/s
5
0
hei
gh
t (m
)
v = 0
v = ?m = 20 kg
Cart+ Earth + Spring
Cart +
Earth
900J
100J
100J100J
1000J
WK3b Answers #3 & 4
3. h = 0.9m
4. Δx = 0.03m
Initial Final
m = 500 gv = 0
k = 100
x = 0.30 m 0
Initial Final
4.5J 4.5JBlock+ Earth+ Spring
Bullet+ Earth
1,531J
? ?
W = -1,531J
Unit VII WK3b Answers
5. a. discuss
b.
c. Working by engine = work done by friction = 1000J
d. Since the Fengine> fk then the box will accelerate: a = 0.5m/s2
6. Δx = 20m 7. b. Fx = 86.6N W = 866J
c. the box is accelerating because Fx > fk
d. Working by friction = 675J
e. discuss
Unit VII WK4 Answers 1. a.
b. F = 180N 2. a. Eg = 6000J b. Ek = Eg = 6000J
c. V = 14.14m/s d. V = 20m/s or 1.4 times more
e. htotal = 40m or 30m higher than the original height
3. V = 16.5m/s 4. V = 33m/s, twice the original velocity
Ek = W
-W doneby glove on ball
ball
h=10m
Δx=0.35m
F=?
Unit VII WK4 Answers
5. Vbullet = 967m/s
6. a. Eint = 1106J
b. See notes
1200J
94J
Eg=mgh Ek=1/2mV2
ChildSlideEarth
Δx=0.85m
V=0m/s V=?W=Ek
WK4 Problem #6
A 24kg child descends a 5.0m high slide and reaches the ground with a speed of 2.8m/s. How much energy was dissipated due to friction in
the process? Do a pie chart analysis of the final state, using
accurate % of the pie to represent the amount Eint in the process.
Power
One of the events in the “World’s Strongest Man” competition is called Atlas Stones. Five stones are placed at the base of five platforms.
Strength or power is judged by the time it takes to complete the task. timetime
WorkP
Energy Units:
J/s = Watts
…also measured in units of horsepower (746W = 1hp)
PHHS Strong Student Competition Find the total work done / energy
exerted and the amount of time to do it.
t
mgh
t
E
t
WP g