1. Energy
Modeling Unit VII

2. 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

3. 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

4. Spring-Force Lab Results40
F (N)
Δd (m) 50 25
0.5 1 20 15 10 5 45 35 30
1.4

5. F = (25N/m) Δd + 2.5N F (N) Δd (m)
How much mass needs to be added to the red spring to stretch it approximately 0.50 m? 40
F (N)
Δd (m) 50 25
0.5 1 20 15 10 5 45 35 30
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 = kg =150 g

6. Hooke’s Law for Springs
General Equation:
“k” = spring constant (strength of spring)
Ideal springs have no preload (F0).
Any amount of force on a spring causes it to stretch.

7. Effort to Stretch Spring
The energy to stretch a spring involves the combination of…
The force of tension in the spring (FT)
The displacement or stretch of the spring (Δx)
How do we represent this force-stretch combination? … or the combination of two values in general?

8. Review: finding displacement (Δd)
If you are moving your displacement depends on 2 things…
How fast you are traveling
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.
During Constant Velocity:
During Acceleration:
Δd = (½)•bh = 9m
Δd = (2m/s)•6s = 12m

9. Representing Effort to stretch a spring:
Effort to stretch spring = area under FT vs. stretch (Δd) graph 40
FT (N)
Δd (m) 50 25
0.5 1 20 15 10 5 45 35 30
Effort =

10. Finding Effort Mathematically
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) =
Area under
The graph

11. Energy Stored in a Spring (Eel)
Eel = Elastic Energy
k = Spring Constant
Δd = displacement or stretch
Joules (J) are the standard units for ENERGY
 A calorie is also a unit of energy.

12. 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)

13. 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

14. 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 $)

15. 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.

16. 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)

17. Worksheet 3a (Problem #1) v1
Define the system as… Spring + Cart + Earth
NO FRICTION
Initial
Final
Spring
+ Cart
+ Earth

18. Worksheet 3a (Problem #1) v2
Define the system as… Spring + Cart + Earth
WITH FRICTION
Initial
Final
Spring
+ Cart
+ Earth

19. Worksheet 3a (Problem #1) v3
Initial
Final
Define the system as… Cart + Earth
NO FRICTION
Cart +
Earth
+ work is done
on the cart by the spring

20. Worksheet 3a (Problem #1) v4
Initial
Final
Define the system as… the Spring
NO FRICTION
Spring
Work is done
on the spring by
the cart

21. 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.

22. 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?
Ek(J)
V(m/s)
Ek (J)
V(m/s) ?
Motion Sensor Δx
m = 0.291kg

23. Kinetic Energy (Ek) 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.

24. Energy Review What is energy? How or where can energy be stored?
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)

25. Gravitational Energy (Eg) Account
To be above the ground something has to do work ON the car to give it some Eg: h
F =_____
Fg = mg
Eg =
g = 10N/kg

26. 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)
m = 0.291kg
h = ?
h = 0m

27. Solving Other Problems
Changing gravitational energy to kinetic energy is useful for solving many different types of problems.
Freefall
Straight
Ramps
Curved
Ramps
Pendulums 1 1 1 1 h 2 2 2 2
The speeds will be the same, but the directions different!

28. WK3a Problem #2 What is the car’s velocity halfway up the loop? 20m
Initial
Final
20m
What is the car’s velocity halfway up the loop?
m = 500kg
k = 8000N/m
Δx = 5m
h = 0m
h = 10m
V = ?
Cart
Spring
Earth

29. WK3a Problem #8
Initial:
Final:
How much force did Super Man use when stopping the train?
m = 100,000kg
V = 22.7m/s
or 50mi/hr
Δx = 50m
V = 0m/s
F = ?
Train
Superman

30. 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

31. WK3b Answers #1 & 2 1. Δx = 2m 2. V = 9.5m/s 100J 100J Cart + Earth
+ Spring 5
height (m)
v = 0
v = ?
m = 20 kg
1000J
900J
Cart +
Earth
100J

32. WK3b Answers #3 & 4 3. h = 0.9m 4. Δx = 0.03m Initial Final m = 500 g
v = 0
k = 100
x = 0.30 m
Block
+ Earth
+ Spring
4.5J
4.5J
Initial
Final
Bullet
+ Earth
1,531J ? ?
W = -1,531J

33. 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 = m/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

34. Unit VII WK4 Answers 1. a. b. F = 180N
Δx=0.35m
Unit VII WK4 Answers
F=?
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
ball
-W done
by glove on ball
h=10m

35. Unit VII WK4 Answers W=Ek 5. Vbullet = 967m/s 6. a. Eint = 1106J
V=0m/s
V=?
5. Vbullet = 967m/s
6. a. Eint = 1106J
b. See notes
Δx=0.85m
1200J
Child
Slide
Earth
94J
Eg=mgh
Ek=1/2mV2

36. 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.

37. …also measured in units of horsepower (746W = 1hp)
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.
Units:
J/s = Watts
…also measured in units of horsepower (746W = 1hp)

38. PHHS Strong Student Competition
Find the total work done / energy exerted and the amount of time to do it.