Download W = F x d = N x m = Energy = Joule

Physics – Energy CH 5 – NOTES
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UNIT Outline:
1. Work
Definition
Force at angles
Units for work
2.Energy
Types: KE, PE,
Derive KE, GPE, and EPE
Calorie Conversion
3.Power
Equation, Units
Horsepower
4.Conservation of Energy
work-energy theorem
Magic can and Pendulum
5.Simple Machines
Types of simple Machines
Efficiency
Simple Machine LAB
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1. WORK
Work: A measurement of the energy used to cause a force to displace an object.
Key words: Force, displacement, and Cause. The force MUST cause the displacement
Examples: Is work being done?
Push a wall - no wall is not displaced
Book falling from desk to floor – Yes, book is displaced by gravity
Is my hand doing work by carrying a book across the room – No, there is a force, but that force doesn’t
cause the displacement.
Dragging book across room – Yes, some of the force is used to displace the book
Dragging a book across room in a circle – No, no displacement.
Running on a treadmill – No, no displacement
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Closer look at work:
W = F x d = N x m = Energy = Joule -> J
A joule is a small number. If one moves a 1N object (.1 kg ~ .2pound object) a distance of 1 m, 1 J of work is
done.
For example, a 100 W light bulb will give off 360,000 J of energy each hour it runs.
W=Fd
However, the force needs to cause the displacement. Therefore
The Force and Displacement MUST be in the same direction
How do we make sure it’s in the same direction? Trig… Cos
Therefore, W = F x d x cos
If all force is in direction of displacement,  = 0, cos = 1
If no force is in direction of displacement,  = 90, cos = 0
Do examples of problems with angles.
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2. Energy
Since work is a measurement of energy, let’s take a closer look at energy
2 types of energy:
KE and PE
KE – Kinetic Energy - energy of motion
PE - Potential Energy - stored energy  This energy can be released to create motion (KE)
Deriving KE equation:
We do work on a ball by throwing it, the ball is in motion.
Lets apply a constant force to the ball for a distance (x) before it leaves my hands. This will cause the motion.
W = Fx
As we throw it, it accelerates.
According to newtons 2nd law, F = ma
Therefore, a = F/m
Once it leaves our hands, it will obtain its final speed.
Vf2 = Vi2 + 2ax
However, the ball is starting from rest, so Vi = 0
Vf2 = 2ax
Let’s substitute what we know for acceleration (a = F/m) into the above equation:
Vf2 = 2 (F/m)x
We are talking about work, so lets solve the equation for work: move F and x to one side
Fx = ½ mVf2
Fx is the work done on the ball by us.
½ mVf 2 is therefore the energy of the ball in motion.
The symbol for the energy of an object in motion is KE (Kinetic Energy)
Therefore, KE = ½ mV2
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Since KE is a measure of energy, it’s units should be the Joule….
Look at units: KE = ½ mV2  kg (m/s)2  kg m2/s2  (kg m/s2)(m)  N m  Joule
Do sample problems
Introducing PE
Lots of types of PE:
CPE – chemical – batteries, digestion, gas, other chemical reactions (you learn this in chemistry class)
EPE – electrical stored energy – capacitors (will look at this later in the year)
GPE – gravitational PE – stored energy due to an objects position
EPE – Elastic PE – stored energy in elastic materials due to their stretching or compressing
Lets look at GPE and EPE
GPE
GPE = Fx = F(grav) x(height) = (m ag ) h
GPE = magh
Since GPE is a measure of energy, it’s unit should be a joule…
GPE = magh  kg m/s2 m  (kg m/s2)(m)  N m  Joule
Do sample problems
Elastic PE
In 1600’s a British physicist names Robert Hook studied springs. He noted a relationship.
The amount by which an elastic substance is deformed is related to the force causing the deformation. This is
known as Hooke’s Law
Kind of common sense, the more force you apply to a spring, the more it will stretch.
Hooke’s Law is quantified as: F = -Kx
X is the deformation (amount the spring is compressed or stretched)
K is the spring constant. This depends on the material the spring is made of, and how the spring is built.
K is measured in force per length (N/m)
(-) sign denoted the force is opposite the direction of displacement. Ex, if you pull a spring apart, it will want
to fly back together.
EPE = ½ KX2
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Again, EPE is a measure of energy, so the units will be Joules. Any energy is measured in joules.
Show different springs: Lab springs, Rubber bands, garage door spring, car shocks
Do spring example, Bungee cord
Putting it together:
Work is a measure of energy. Therefore, work equals energy, so you can set it = to KE or PE.
W = KE  Fx = ½ mV2
W = PE  Fx = m ag h
Or
Work can measure the change in energy:
W = KEf – KEi
Do sample problems:
3 kg hammer hits a nail at 3 m/s. The nail goes .5 cm into the board. What is the average force on the nail?
m = 3 kg
x = .005 m
F=?
V = 3 m/s
W = KE
Fx = .5mV2
Solve for F, convert weight to mass
F = (.5mV2) / x = (.5 3 32) / .005 = 2700 N
The hammer hits with a force of 2700 N, which is a large number – a few hundred pounds of force.
seems reasonable, since if you hit your thumb with a hammer it will smash it.
This
One last note:
Another common unit for energy instead of the Joule is the Calorie.
1 Dietary Calorie = 1000 Calories
1000 cal = 4200 J or 1 cal = 4.2 j
On the dietary list on foods, in the United states we use Dietary Calories. Most other countries use regular
Calories. This similar to how we use the English system, everyone else uses the metric system…
Disclaimer: The types of food we eat Digest differently, some digest more efficiently than others. For
example, Calorie for calorie, fat, carbohydrates, and protein, give you slightly different amounts of energy.
Calorie Example:
How much energy will eating a 200 calorie cereal bar give an 80 kg person?
200 dietary calories = 200,000 cal. 200,000 cal x 4.2 = 840,000 j
Sounds like allot, but a 100 W light bulb used 360,000 j per hour. The unit Joule is a small number.
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If 30% of that energy is used for motion, and the 80 kg person climbs up a 1 km tall mountain side, will this
cereal bar give him enough energy?
30% of 840,000 j = 252,000 j
PE = M ag h = 80 9.8 1000 = 784, 000 j
No, the person will be short on energy.
3 Power
Sometimes it is not convenient to analyze the amount of work done.
Why? What is “Work” missing?? TIME
Often it is more convenient to express work in terms of time.
Physicists use Work/Time
POWER = Work/Time (P = W/t)
Units is J/s = Watt
(James Watt)
Ex, Light bulbs are measured in watts
Sample1: 2 students lift 75 kg weights. They both lift it 2 m into the air. However student A takes 2 seconds
to lift it, while student B takes 5 seconds to lift it. Which student does more work? Which student is more
powerful?
P = w / t  student A: (75)(9.8) (2) / 2 = 735 W
Student B: (75)(9.8) (2) / 5 = 294 W
Sample2:
You are helping design a theater stage. A 193 kg curtain on the stage needs to be raised 7.5 m at a constant
speed in about 5 s. There are 3 motors available for purchase. A 3.5kW, a 5.5 kW, and a 1 kW motor. Which
motor should you choose to install on the stage?
P = W / t = (193) (9.8) (7.5) / 5 = 2837 W = 2.8 kW  So, the 3.5 kW will work the best.
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If we play with units, we can get a convenient equation:
P = W/t = F x / t = F v
Therefore, P = W/t = F v
So if one knows the force applied and the velocity of the object, on can determine the power output. This is
VERY convenient for finding the power of engines in cars, planes, boats, etc…
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HORSE POWER
One last thing with power:
When dealing with engines, we rarely use W or kW. What do we usually hear? HorsePower
Interestingly enough, James Watt coined the unit Horsepower.
James Watt fine tuned the Steam Engine, the first types of engines invented in the 1700’s. He obviously
wanted to make money by selling his steam engines. The best market for his steam engines were farms and
mines, where horses would lift coal out of mines, or spin wheels in order to pump water or grind wheat corn,
etc..
Farmer Joe knew nothing of the Watt unit. So James Watt would have a tough time selling them engines to
replace their horses if he used unfamiliar terms.
Watt decided to study workhorses. He determined that 1 horse on average could lift 330 pounds of coal per
minute. OR 1000 lbs of coal 33 feet in 1 minute.(Watt was British). So he said 1 Horsepower = 33000 foot-lbs
per minute
Now, Watt looked at his engines and did some calculations. 1 HP = 746 Watts
So, now James could go to the farmers and mine owners and say, If you buy my
1500 W engine, can replace 2 of your horses. My engines don’t need stables, food, sleep, etc. Just ethanol to
run and a little oil now and then.
Although almost no one uses horses today, the unit HP stuck. It’s on our cars, lawnmowers, vacuum cleaners,
etc…
Just imaging, a ford commercial, where instead of the truck driving in Montana with a herd of horses, it’s
driving through light bulbs. For marketing reasons, companies love the term Horsepower. Change the name of
a Ford Mustang to a Ford Bulb. Not going to happen.
Example of using Horsepower.
Ex: What is the horsepower of a 1200kg car that can go from 25 km/hr to 100 km/hr in 6 s?
First, convert to standard units!
25 km/hr = 6.9 m/s
100 km/hr = 27.8 m/s
Power = W / t, so find W first:
Find change in energy:
W = Kef – KEi = (½ 1200 6.92) - (½ 1200 27.82 ) = ½ 1200 (47.6-772.8) = ½ 1200 725.2 = 435,144 j
Now find Power:
P = W/t = 435144 J / 6s
P = 72.5 kW
Convert to HP
1 hp = 746 W
72.5 kW = 97 HP  So, this car engine produces 97 HP
assignments: Work&Power I wksht , WorkKE wksht
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Kowinsky
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3. Conservation of Mechanical energy:
Total energy of a system remains constant
ENERGYtot = KEtot + PEtot
Or
ENERGY in = ENERGY out + waste
Therefore:
KEin + PEin = KEout + PEout + waste
Total energy is conserved.
There is always wasted energy. Sound produced, heating, deformation, light, etc… all of this produces waste
energy.
Energy can change forms, but always remains constant in a system.
Bouncing a ball, if a rubber ball is dropped, it will never reach the origional height. Energy is lost.
“magic can” demo
Pendulum Demo
Diving board diagram on chalkboard
Do examples:
Skier going down slope. What is skiers final V at bottom of slope (don’t use kinematics). Lets ignore friction
for now, so no waste energy
Lets say the ski slope is 20 m tall.
Kein + PE in = Kef + Pef
0 + mag h = 1/2mv2 + 0 
0 + m 9.8 20 = ½ m v2 + 0
Clean it up a bit… mass cancels:
(9.8)(20) = 1/2v2
 solve for v  v = sqrt( (9.8)(20)(2) ) = 19.7 m/s
In reality, there would be waste energy… friction, so the answer would be smaller.
Sliding Board:
Physics – Energy CH 5 – NOTES
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Person slides down a slide. It is 3 m tall. The person however, takes a running start down the slide at a speed of
2 m/s. What is the persons final velocity at the bottom?
Kei + Pei = Kef + Pef
1/2m22 + m(9.8)(3) = 1/2mv2 + 0
Mass cancels…
(½)22 + (9.8)(3) = 1/2v2  2 + 29.4 = .5v2  31.4 = .5v2  v = sqrt((31.4)(2)) = 7.9 m/s
Bungee jumper example:
Bungee Jumping minitopic
You are designing a Bungee jump. You are on a 70 m tall bridge, and, at the fullest stretch, want to land 4 m
from the ground. (4 m safety cushion). M = 60 kg. K = 25 N/m , How long of a cord do you need?
Initial Conditions: KE = 0, at rest, EPE = 0, not stretched, GPE = 100%
Final Conditions: KE = 0, at rest again, EPE = some % stretched, GPE = some number
Equation:
GPE = GPE + EPE
m 9.8 hi = m 9.8 hf
+ ½ K X2
(60)(9.8)(70) = (60)(9.8)(4) + ½ 25 X2
41160 = 2352 + ½ 25 X2 
41160 – 2352 = 12.5X2  38808/12.5 = X2
X  X = sqrt(3104.6) = 55.7 m
Therefore, the cord stretches 55.7m. This is not the answer. The bridge is 70 m tall, and you want to stay 4 m
from the ground…. 66 m – 55.7 m = 10.3 m
You would need a 10.3 m bungee cord with a spring constant of 25 N/m
What if the person had a mass of 70 kg. What length of cord would this person need for the same distance?
Do the math again, replace mass by 70 kg… 5.8 m cord.
Assignment:
Conservation wksht
QUIZ
Physics – Energy CH 5 – NOTES
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Kowinsky
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4. Efficiency and Simple Machines:
A machine is a device that decreases the amount of force needed to displace an object.
!It does not decrees the amount of work!
Examples of simple machines:
Pulley
Do pulley demo
Inclined Plane
Zig zag road going up a mountain, a wedge, a wheelchair ramp
Screw
Create screw from inclined plane
Wheel and Axel
Show wheel and axel, wrench, gear on bycicle
Fulcrum (Lever)
Crow bar, Human arm, door handle,
The power delivered by a machine of any kind is always less than the power supplied to it. This is due to
friction and waste energy. You can never get more energy out of a machine than what you put into it.
Efficiency is the ratio between power out and power in
or
work out and work in
Eff = Pout / P in
Or
Eff = Wout / W in
Efficiency can never be over 100%. This means energy cannot be created. Also, in real life, Efficiency is not
100%, it is always lower since there is always waste energy. In real life situations, efficiency is often MUCH
lower than 100%
Example:
Car: 7%  93% is lost in mostly heat . Now, most of that 7% is used to physically move the car. To
physically move a passenger (the point of a car), the efficiency drops to 0.3%.
Hybrid car is about ~10% efficient
Electric Car ~40-50% efficient
Water Heater ~ 50% efficient (very rough estimate)
Tankless water heater ~ 80% efficient
A human: Walking ~ 25% efficient
Running ~50% efficient (Because muscles act as springs, you get elastic energy conversion)
Mice: 3% efficient at running – they are not designed to run  they scamper!
Compound machines are composed of many simple machines put together.
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Sample Problems Dealing with Efficiency:

When doing efficiency problems, students often confuse the output and the input.
Output is what the actual machine does – the energy given off by the machine.
Input is what the person, or motor, must do – the energy put into the machine.
Ex1: Pulley sample:
A compound pulley is used to raise a 50 kg object a vertical displacement of 3 m. For this to occur, a person
must pull a rope with a force of 100N a displacement of 15 m. Calculate the efficiency of this pulley.
Fout = 50 x 9.8 = 490 N
Xout = 3 m
Fin = 150N
Xin = 15 m
Eff = Wout / Win = (Fo Xo) / (Fi Xi) = (490N) (3m) / (120N) (15m) = 1470 j / 1800 j = .82
The pulley is 82% efficient
Ex2:
A crane whose motor has a power input of 5 Kw raises a 1200 kg beam through a hight of 30 m in 90 s.
Calculate the efficiency of the crane.
Pin = 5000 W , x = 30 m, t = 90 s, m = 1200 kg
Eff = Pout / Pin
Find Pout, and plug into above equation:
Pout = W / t = (F X) / t = ((1200 9.8)(30)) / (90) = 3920 W
Plug into Eff equation:
Eff = Pout / Pin = (3920 W) / (5000 W) = .784 = 78%
The crane has an efficiency of 78%, that means 22% of it’s energy is wasted.
Ex3:
A trash compactor has a .25 HP motor. It can apply 4500 N of force (1 ton crushing force). The machine is
80% efficient. How fast does the compactor move?
Eff = .80
Pin = .25 HP x 746 W = 186.5 W
Fout = 4500 N
Vout = ?
Eff = Pout/Pin However, P = F v - so, solve for v.
Eff = F v / Pin  v = (Eff) (Pin) / (F)  v = (.80) (186.5W) / (4500 N) = .03 m/s
This is a slow velocity, but it’s a trash compactor, they move slow. The power is used in the force, not
the velocity.
Simple Machine Lab
Assignment: Review sheet
EXAM