Download work and energy

WORK AND ENERGY
Another Way to Look at Motion

The most important concept in science!
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

What is energy?
Difficult to define precisely.
 Exists in many different forms

Work
The product of the magnitude of
displacement times the component of force
parallel to displacement
 W = Fd

F
d
Work(more precisely)
The product of the magnitude of
displacement times the component of force
parallel to displacement
 W = Fpd cos q

F
q
d
Units of Work and Energy
SI unit – newton-meter = joule
 1 J = 1 n –m
 Obsolete units you might run across:

– In cgs system unit is erg = dyne-cm
– In British system ft-lb
– 1 J = 107 ergs = 0.7376 ft-lb
Who Does More Work?

A weightlifter holding
up 200Kg

A baby lifting a
feather

(Force, no
displacement)

(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


Work or no work?
Lifting force is up, but displacement is horizontal;
therefore……
No work is done on refrigerator
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
Only up component of
displacement contributes
Work Done By Sun on Earth

How much is there?
NONE!
FG
v
ENERGY
The ability to do work (an imperfect
definition)
 Many types exist: mechanical (potential,
kinetic), heat, light, 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
Mechanical


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
 TRANSLATIONAL: KE = ½ m v2

Derivation of ½ mv2
Consider a mass accelerated uniformly from
rest to velocity v
 Work done = W = F x d
 F = ma
 W = mad
a = (v2 – v02)/2d
 v2 = v02 + 2ad;
 W = m d (v2 – v02)/2d = ½ mv2


(v0 = 0)
Derivation of ½ mv2
Consider a mass accelerated uniformly from
rest to velocity v
 Work done = W = F x d
 F = ma
 W = mad
a = (v2 – v02)/2d
 v2 = v02 + 2ad;
 W = m d (v2 – v02)/2d = ½ mv2


(v0 = 0)
Examples
Find the kinetic energy of a 70 kg person
walking at 1.0 m/s.
 KE = 1/2mv2 = 35kg x (1m/s)2 = 35J

Find the kinetic energy of a 0.01 kg bullet
traveling at 1000 m/s.
 KE = 1/2mv2 = 0.5 x 0.01 x (1000m/s)2
 KE = 5000J

Why is it so dangerous to get
shot?
Bullet deposits lots of energy in small area
 What about momentum (mv)?
 Find momentum of man


70 kg m/s
Find momentum of bullet
 10 kg m/s

Why is a comet or asteroid crash
on Earth so dangerous?
Find the kinetic energy of a 1014 Kg
asteroid whose speed is 50 km/sec.
 KE = ½ mv2 = 0.5 x 1014 x (5 x 104 m/s)2 =
12.5 x 1022 J = 1.25 x 1023 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

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 = 50,000 J = 5 x 104 J

Force Required
What average force is needed to do this if
the distance is 100m?
W=FxD
 F = W/D = KE/D = 50,000 / 100 = 500N

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
Gravitational Potential Energy
An object held high has the potential to do
work
 PEgrav = mgy
 Reference level of zero PE is arbitrary

How Much PE?





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
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
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

Conservation of Mechanical
Energy
In absence of friction or other nonconservative forces
 KE + PE = constant

Conservative Force
Work done does not depend on path taken
 Potential energy can be defined
 Example: lifting an object against gravity

Non Conservative or Dissipative
Force
Work done depends on path
 No potential energy function can be defined
 Example: pushing an object against friction
 W = Fd = mFNd = mmgd

Power
The rate that work is done
 P = work/time = Fd/time = Fv
 Unit joules/sec = watt
 746 watts = 1 horsepower

Power
The rate that work is done
 P = work/time = Fd/time = Fv
 Unit joules/sec = watt
 746 watts = 1 horsepower

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




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