Energy

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


Initial


as… Spring + Cart + Earth

WITH FRICTION

Spring+ Cart + Earth


Initial


as… Cart + Earth NO FRICTION

Cart +

Earth

+ work is doneon the cart by

the spring


Initial


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

Energy

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