Download WORK AND ENERGY

WORK & ENERGY
Another Way to Look at Motion
What’s so Great About Energy?
It’s a scalar; forget those vector headaches
 It’s useful in all of physics and in other
sciences
 It’s conserved, meaning the total amount of
it doesn’t change

Work
The product of the magnitude of
displacement times the component of force
parallel to displacement
 W = Fd

F
d
Units of Work and Energy
SI unit – newton-meter = joule
 1 J = 1 n –m (kg m/s2·m)
 Obsolete units you might run across:

– In cgs system unit is erg = dyne-cm (spring scales)
– In British system ft-lb (torque wrench)
– 1 J = 107 ergs = 0.7376 ft-lb
Who Does More Work?

A weightlifter holding
up 200Kg

A baby lifting a
feather
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(Force, no
displacement)
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(Small force, some
displacement)
Who Does More Work?

A weightlifter holding
up 200Kg

A baby lifting a
feather

(Force, no
displacement)
No Work!

(Small force, some
displacement)
Some work

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Work or no work?
Lifting force is up, but displacement is horizontal;
therefore……
No work is done
Work or No Work
A mass circles at
constant speed, held by
a string
Force is along
string, toward
center
Force is
perpendicular to
motion
Therefore, no
work is done
Calculate the work
20 Kg crate is pulled 50m horizontally by a
100N force
 W = Fd = 100N x 50m = 5000Joules

FN
F = 100N
mg
Work to Climb a Mountain
Work = force x distance
How much work is
required for a 70 Kg
person to climb
1000 m up a peak?

Hint: use F = mg
Answer : 6.86 x 105 J
ENERGY
The ability to do work (an imperfect
definition)
 Many types exist: potential, kinetic, heat,
electrical, magnetic, nuclear
 They can change from one to another
 The sum of all of them (total energy)is
conserved

Energy Conversion Example

What form of energy comes into the
projector?
Answer: electrical

What forms are produced?
Answer: light, heat, sound, kinetic, magnetic
Common Forms of Energy


Kinetic – energy of
motion
Potential – energy of
position
A pendulum converts energy
back and forth from potential
to kinetic.
Law of Conservation of Energy
In any process total energy is neither
decreased nor increased
 It can change from one form to another
 It can be transferred from one body to
another, but
 IT CAN NOT BE CREATED NOR
DESTROYED

Kinetic Energy
Energy of Motion
 Translational and rotational
 KE = ½ m v2

How Much PE?

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How much PE does a
100kg crate get when
raised 100m?
PE = mgh use g = 10
N/kg
PE = 100kg x 10N/kg
x 100m
PE = 100,000 J
PE = 1.0 x 105 J
Work-Energy Principle
The net work done on an object equals the
change in its kinetic energy
 Wnet = DKE
 Work that increases KE is positive
 Work that decreases KE is negative

Gravitational Potential Energy
An object held high has the potential to do
work
 PEgrav = mgy
 Reference level of zero PE is arbitrary

Examples
Find the kinetic energy of a 70kg person
walking at 1.0 m/s?
 KE = 1/2mv2 = 35kg x (1m/s)2 = 35J

Find the kinetic energy of a 0.01kg bullet
traveling at 1000m/s
 KE = 1/2mv2 = 0.5 x 0.01 x (1000m/s)2
 KE = 5000J

Roller Coaster
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What speed will a frictionless roller coaster have
at the bottom of a 40m high hill assuming zero
speed at the top of the hill?
PE lost = KE gained
mgh = ½ mv2
2gh = v2
v = (2gh)1/2
v = (2 x 10 x 40)1/2 = (800)1/2
Answer v = 28 m/s
Work Lab

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Set up a block and tackle machine with various amounts of pulleys.
Carefully place 10 weights on the bottom tackle block, also arrange the
pulley string in as many different combinations as possible.
Arrange the pulley string (yellow one) with just one strand, then use a force
meter and pull to the top to find the weight of the tackle block. Fill in the
data table. Force in(you) - Force out (weight)
Strands
(passes you
made
around
pulley)
1
Total
Mass=
block +
weights
Distance
(Length
you pull)
Force In
(You)
Force Out
(Wt lifted)
Work =
Fin x d
M.A. =
Fout/Fin
Work Example

If you shove a box with a force of 100 N and it
moves 5 m, what amount of work have you
done?

If you pull the same box above with a force of
100 N at an angle of 30⁰ and it moves 10 m,
what is the amount of work done on the box?
(Hint: work is always in the direction of the
motion, so use Fx only, so use W = F cos Θ x d)
Energy Conversion Example
Remember in a system where only gravity is acting
(like in a roller coaster), The potential energy is
converted into kinetic energy and vice versa.
1.
If a 10,000 kg roller coaster is raised 100m off
the ground:
a. What potential energy will it have at the top?
b. What velocity will it have at the bottom?
c. What velocity will it have half way down?

How Much Work?
Is needed to give a car of mass 1000kg a
speed of 10 m/s?
 W = Kinetic Energy gained
 W= ½ mv2
 W = 0.5 x 1000kg x (10m/s)2
 W = 50,000J

How Much Work…

is required to accelerate a 1000Kg car from
30 to 40 m/s?

Use W = 1/2mv22 - 1/2mv12
Answer:
3.5 x 105 joules
Conservation of Mechanical
Energy
In absence of friction or other nonconservative forces
 KE + PE = constant

Simple Machines

Machines that make work easier by
increasing force or increasing distance
All simple machines trade force for distance;
they can’t increase both
Examples of Simple Machines
Lever
 Inclined Plane
 Screw
 Gear
 Wheel and Axle
 Pulley

Lever
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See saw
Pry bar
Screw driver used to
pry
Fork, pencil
Paint brush
Which of these
increase force?
Courtesy
www.lkwdpl.org/schools/elempath/
simplemachines
Inclined Plane
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Ramp
Knife
Road up hill
Screwdriver pushed in
Courtesy
www.disabled.driverinfo.btinternet.co.uk
/ acctocar.html
Screw

Inclined plane
wrapped around a
cylinder
Q: Is a screwdriver an example
of a screw?
Courtesy www.uen.org/.../
view_activity.cgi?activity_id=6528
Gear
Wheel with teeth that mesh
 Changes speeds
 Increases or decreases force
 Used in auto and marine transmissions

Wheel and Axle
A lever wrapped in a circle
 Axle is normally fixed to wheel

Pulley


Axle turns freely
Types:
– Single fixed
– Single moveable
– One fixed one
moveable
– Block and tackle
Courtesy www.conductortrain.com/.../apprentice/ skills/doc9.shtml
Work In = Work Out
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In absence of friction the work you put into a
simple machine equals the work that comes out
Fin Din = Fout Dout
Fout/ Fin = Din/ Dout
Illustrates the trade-off between force and distance
You can’t get “something for nothing without
violating conservation of energy
Mechanical Advantage
Fout/ Fin is called “mechanical advantage,”
actual mechanical advantage(AMA) to be
exact.
 Din/ Dout is called ideal mechanical
advantage (IMA)
 In a real machine AMA is always less than
IMA because of friction

Small and Large Mechanical
Advantage

Machines that increase force greatly are
said to have large mechanical advantage
– Example – pry bar

Machines that increase distance and
decrease force have mechanical advantage
less than one
– Example – paint brush
Efficiency
 AMA
= e x IMA
e
is called efficiency
 All machines have an efficiency
less than one so as not to violate?
Energy Conservation!
Lever Example

A certain lever lifts a weight of 20N with an
effort force of only 5N. Assuming ideal
efficiency, over what distance will the effort
force act to lift the weight by 0.1 meter?
Answer: 0.4m
Pulley Example

A pulley system has an ideal mechanical
advantage of 2.
– (a) What effort force will be required to lift
500N? 250 N
– (b) if the efficiency is only 80%, would more
force be required or less? more
Review

Why can’t a simple machine have an
efficiency greater than 1 (100%) ?
It would violate the law of conservation of energy.
Compound Machines

Many real machines
are combinations of
simple machines
Power
The rate that work is done
 P = work/time = Fd/time = Fv
 Unit joules/sec = watt
 746 watts = 1 horsepower

Power to Climb a Hill

A 60 Kg student climbs a 100m high hill in
three minutes. Find the student’s power in
watts and horsepower.
Answer 326w, 0.44hp
Power Needed by a Car
A 1400 Kg car runs over level ground at
30m/s. If 1000N force is needed to keep it
moving, what power is required (watts and
HP)
 P = Fv =
 1000N x 30m/s = 30,000 watts=
 30,000w ÷ 746 w/HP = 40HP

Efficiency Lab- Show all work and data chart!
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Place Photogate as far down the ramp as possible.
Use your spring scales and record the mass of the car.
Place car at top of the track, measure and record the
height above the table from middle of car.
Release the car and calculate the speed through the
bottom photogate.
Calculate the PE at the top and the KE at the bottom of
the ramp.
In theory, these should be the same.
Efficiency= Eout (KE)/ Ein(PE) Calculate for your trial.
Repeat entire experiment with 1, 2 and then 3marbles in
car.
Answer questions 4 c and d on p. 82 in lab book!
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Power Lab
Make a data table just for you!
Record you weight in lbs and Newtons. (1 lb= 4.45 N)
Calculate the distance you will travel (25 steps, each step .16 m) record
With the help of a partner, time yourself walking,
running and jumping UP the stairs- record
Calculate the Work done for each trial (W = F x d)
Calculate the Power of each trial ( P = W/t)
Convert the Power in Watts to Power in hp (divide Watts by 746)
Calculate the total Work done during the Lab
Convert the total work to Food Calories:
(1 cal= 4.2 J and 1 Food Cal= 1000 calories)
a) Divide by 4.2 b) Divide by 1000
If you wanted to work off 1 Big Mac (550 Food Calories) How many
times would you have to repeat the entire lab?