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# Work_ Energy and Power

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```									Work, Power & Energy

Basic Terminology and Concepts
Review

   Newtons Laws
   Used to analyze motion of an object
 Net force on a mass  acceleration
 Acceleration  change in velocity over time

   Used to predict final state of an object's
motion

What are other ways to look at motion?
Motion Based on Work and Energy

   Objective:
 Understand and calculate the effect of work
on the energy of an object (or system of
objects)
 Predict the resulting velocity and/or height
of the object from energy information
Basic Terminology

   Work
   Total mechanical energy
   Potential energy
   Kinetic energy
   Power
Work

   A force acting upon an object to cause a
displacement

   For a WORK to be done:
 1. Displacement MUST happen
 2. Force MUST cause the displacement

 3. Force and displacement must be parallel

What are some examples of work?
Examples

 a horse pulling a plow through the fields
 a father pushing a grocery cart down the
aisle of a grocery store
 a freshman lifting a backpack full of books
   (would a junior do work like this?)
 a weightlifter lifting a barbell above her head
 a shot-putter launching the shot, etc.

 climbing a flight of stairs
Work
Work or NOT?
   A teacher applies a force to a wall and
becomes exhausted.

   A book falls off a table and free falls to the
ground.

   A rocket accelerates through space.

   No. The wall is not displaced.

   Yes! The is a downward force (gravity)
which acts on the book to displace it.

   Yes. The expelled gas is the force which
accelerates the rocket through space.

   A waiter carries a tray full of meals
above his head by one arm across the
room.

   Consider the following:
 In which direction is the force exerted on the
tray?
 Which direction does the tray move?
 Are those directions parallel?
Answer: We need to be specific
because there are two forces.
 The normal force is exerted vertically on the tray.
 The tray moves horizontally.
 Since those are not in the same direction, there
is no work done on the tray by the normal force.

 There is a horizontal frictional force in the same
direction as the horizontal displacement.
 Therefore, friction does work on the tray!
A Force Does NO WORK When It Is
Perpendicular to the Displacement
Force at an Angle
 The tension in the chain
pulls upward and rightward.
 Fido moves rightward.
 Only the horizontal part
(component) of the tension
does work on Fido.
 The ANGLE determines the
component of the force
which actually causes a
displacement.
 We won’t do this
mathematically.
Which angle is used?

   The angle between the force vector and
the displacement vector.

   NOT the angle of
ascent in this case

 Direction of pull =
Displacement direction
Describing Work Mathematically
   Work = Force x Displacment   W = F*d

   Force and displacement
are rightward.  WORK
IS DONE!!!

   Force left, displacement
right.  NEGATIVE
WORK IS DONE!!!

   Force up, displacement
left.  NO WORK!!!

When angle = 0 or 180°, WORK IS DONE!
Perpendicular force

   REMEMBER!
   A vertical force
CANNOT cause
horizontal
displacement!

When angle = 90°, NO WORK IS DONE!!!
Work and Gravity

   Work = Force * displacement

   When something freefalls, the force it
exerts is m*g (mass * acceleration due to
gravity). g = -9.8 m/s2.

   Displacement of object is height (h).
   Work = m*g*h
Units of Work (and Energy)

   The joule (J)
   1 joule = 1 newton*meter

   1 J = 1 N*m

Each set of units is equivalent to a force unit times a displacement unit.
Summary

   Work is a force acting upon an object to
cause a displacement.
   Three quantities must be known in order to
calculate the amount of work.
 Force
 Displacement

 Angle between the force and the displacement.

   If angle is 90°, NO WORK IS DONE!!!
Power

 When you exert a force over a distance,
that is called work.
 But… work takes time!

   Does the amount of work change if you
do it over an hour vs. in 5 minutes?
Power Calculation

Power is the rate at which work is done

Power = Work / time
P=W/t
Units of Power

Units of Power = Units of Work / Units of Time
= joules / second

1 joule / second = 1 watt

Units of Power: watts (W)

Joules/sec = Watts!
Machines
   Machines change the magnitude and/or
direction of forces.
   “multiplying the force”
   can also multiply the distance
   Work is CONSERVED
   work input = work output
   (F*d)input = (F*d)output
   So if we can’t get any free work out of the
deal, why bother?
Machines

   Machines can make work easier
 Less input force & more input distance
 More output force & less output distance
   Examples: using a jack to lift a car
   Machines can increase speed
 More input force & less input distance
 Less output force & more output distance
   Examples: bicycle gears

   Mechanical Advantage: how much a
machine multiplies force or distance

output force input distance
input force output distance
   Calculate the                        Equation:
of a ramp that is 5.0 m                 mech. adv. 
output distance
long and 1.5 m high.
   Given:                           Plug & Chug:
   input distance = 5.0 m
5m
   output distance = 1.5
m
1.5 m
   Unknown: mechanical
Simple Machines
Simple Machine   How Does It   Examples
Work?
Lever
Pulley
Wheel & Axle
Inclined Plane
Wedge
Screw
Work and Energy

What is the relationship?
Objectives
   Explain the relationship between energy and work
   Define potential energy and kinetic energy
   Calculate kinetic energy and gravitational potential
energy
   Distinguish between mechanical and non-
mechanical energy
   Identify non-mechanical forms of energy
What is Energy?

 Energy: the ability to do work
 Units: joules, J (same as work)

   Why?
   Definition of work:
 Transfer or transformation of energy
 Transfer is often from one system to another

   It takes ENERGY to do WORK!!!
Work – Energy Example

   Rubber band or slingshot or bow
   You stretch the rubber band.
   Energy is transferred from you to the band.
   Do you do work on the rubber band?
   You release the rubber band.
   Energy is transferred from the rubber band to the
projectile.
   Amount of energy transferred is measured by “work”
done on the projectile.
   Transfer of Energy (bow & arrow):
   Work on bow  Energy in bow  Work on arrow
Potential Energy

   How does the rubber band get
energy?

   Where is the energy in the stretched
rubber band?

   Where is the energy upon release?
Potential Energy

   Def: stored energy; energy of position
   Results from the relative position of
objects in the system.
   rubber band: distance between the two ends
   Stored energy occurs if something is
stretched or compressed (elastic)
 clock spring
 bungee cord
Gravitational Potential Energy

   Gravitational potential energy:
   PE that an object has by virtue of its
HEIGHT above the ground

 GPE = mass x freefall acceleration x height
 GPE = mgh = (Fd)
 mg = weight of the object in Newtons (F)
 h = distance above ground (d)

   GPE stored = Work done to lift object
GPE Example - Solved
 A 65 kg rock climber       Equation:
ascends a cliff. What is     PE = mgh
the climber’s
gravitational potential    Plug & Chug:
energy at a point 35 m
PE = (65 kg)(9.8 m/s2)(35 m)
above the base of the
cliff?
Given:
GPE = 22000 J
m = 65 kg
h = 35 m
Unknown: GPE = ? J
GPE Example - Unsolved
   What is the gravitational   Equation:
potential energy of a 2.5     GPE = mgh
kg monkey hanging from
a branch 7 m above the
jungle floor?               Plug & Chug:
GPE = (2.5 kg)(9.8 m/s2)(7m)
Given:
m = 2.5 kg
GPE = 171.5 J
h=7m
Unknown: GPE = ? J
Kinetic Energy

 Def: the energy of a moving object
due to its motion
 Moving objects will exert a force upon
impact (collision) with another object.

 KE = ½ (mass) (velocity)2
 KE = ½ (mv2)
The Impact of Velocity

   Which variable has a greater impact
on kinetic energy: mass or velocity?
   Velocity! It’s SQUARED!
   Velocity as a factor:
   Something as small as an apple:
 At a speed of 2 m/s = 0.2 J
 At a speed of 8 m/s = 3.2 J
(4 x velocity = 16x energy)
KE Example - Solved

 What is the kinetic      Equation:
energy of a 44 kg            KE = ½ mv2
cheetah running at
31 m/s?                  Plug & Chug:
Given:                  KE = ½ (44 kg)(31 m/s)2
m = 44 kg
KE = 21000 J
Unknown:
KE = ? J
KE Example - Unsolved

 What is the kinetic      Equation:
energy of a 900 kg           KE = ½ mv2
car moving at 25
km/h (7 m/s)?            Plug & Chug:
 Given:                KE = ½ (900 kg)(7 m/s)2
   m = 900 kg
   v = 7 m/s
   KE = 22050 J
   Unknown: KE = ? J
Conservation of Energy

   Objectives
 Identify and describe transformations of
energy
 Explain the law of conservation of
energy
 Where does energy go when it
“disappears”?
 Analyze the efficiency of machines
Other Forms of Energy

   Mechanical Energy – the total energy
associated with motion
 Total Mechanical Energy = Potential Energy
+ Kinetic Energy
 Examples: roller coasters, waterfalls
Other Forms of Energy

   Heat Energy – average kinetic energy of
atoms & molecules
 The faster they move, the hotter they get!
 Ex. Boiling water
Other Forms of Energy

   Chemical Energy – potential energy
stored in atomic bonds
 When the bonds are broken, energy is
released
 Ex. Combustion (burning), digestion,
exercise
Other Forms of Energy

   Electromagnetic Energy – kinetic
energy of moving charges
 Energy is used to power electrical
appliances.
 Ex. Electric motors, light, x-rays, radio
waves, lightning
Other Forms of Energy

   Nuclear Energy – potential energy in
the nucleus of an atom
 Stored by forces holding subatomic particles
together
 Ex. Nuclear fusion (sun), Nuclear fission
(reactors, bombs)
Conservation of Energy

   The Law of Conservation of Energy
   Energy cannot be created nor destroyed,
but can be converted from one form to
another or transferred from one object to
another

   Total Energy of a SYSTEM must be
CONSTANT!
Conservation of Energy

   Total Mechanical Energy = Kinetic + Potential
   TME = KE + PE
 TME must stay the same!
 If a system loses KE, it must be converted to
PE
 In reality… some is converted to heat
 We will USUALLY consider frictionless
systems  only PE & KE
Energy Conversions in a
Roller Coaster
   Energy changes form many times.
   Energy from the initial “conveyor”
   Work stored: Grav. Potential Energy
   Some PE is converted to KE as it goes down
   Some KE is converted to PE as it goes up
   Where does the coaster have max. PE?
   Where does the coaster have min. PE?
   Where does the coaster have max. KE?
   Where does the coaster have min. KE?
   Where could energy be “lost”?
   Friction, vibrations, air resistance
Conservation of Energy:
Example Problem
 You have a mass of 20          Equations:
kg and are sitting on             TMEi = TMEf
your sled at the top of a
 PEi + KEi = PEf + KEf
40 m high frictionless
hill. What is your
velocity at the bottom of          PE = mgh
the hill?                          KE = ½ mv2
 Given:
 m = 20 kg
 hi = 40 m
 vi = 0 m/s
 Unknown:
 vf = ?
Efficiency

   Does work input always equal energy output?
   NO! Energy may be “lost” to friction.
   No machine is perfect!
   Efficiency: a quantity, usually expressed as a
percentage, that measures the ratio of useful
work output to work input

efficiency = useful work output / work input
Efficiency
   A sailor uses a rope and an         Equation:
old squeaky pulley to raise a    Efficiency = useful work output /
sail that weighs 140 N. He           work input
finds that he must do 180 J of
work on the rope in order to        Plug & Chug:
raise the sail by 1 m (doing
140 J of work on the sail).
What is the efficiency of the    Efficiency = 140 J / 180 J = 0.78
pulley?
   Given:                           Efficiency = 0.78 x 100% = 78%
 Work input = 180 J
 Useful work output = 140
J                                  Efficiency = 78%

   Unknown:
 Efficiency = ? %

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