Download Work, Power, and Machines

Work, Power, and Machines
Physical Science – Unit 7
Chapter 9
Work
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• What is work?
– Work is the quantity of energy transferred by a
force when it is applied to a body and causes
that body to move in the direction of the force.
• Examples:
– Weightlifter raises a barbell over his/her head
– Using a hammer
– Running up a ramp
Work
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Work in simple terms:
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• Transfer of energy that occurs when a force
makes an object move
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• The object must move for work to be done
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• The motion of the object must be in the
same direction as the applied force
Work
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• The formula for work:
– Work = force x distance
–W=Fxd
• Measured in Joules (J)
– Because work is calculated as force times
distance, it is measured in units of newtons
times meters (N●m)
– 1 N●m = 1 J = 1 kg●m2/s2
• They are all equal and interchangeable!
James Joule - English scientist and inventor 1818-1889
Work
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• 1 J of work is done when 1N of force
is applied over a distance of 1 m.
• kJ = kilojoules = thousands of joules
• MJ = Megajoules = millions of joules
Practice problem
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A father lifts his daughter repeatedly in the
air. How much work does he do with each
lift, assuming he lifts her 2.0 m and exerts
an average force of 190 N?
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W=Fxd
Practice problem
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A father lifts his daughter repeatedly in the
air. How much work does he do with each
lift, assuming he lifts her 2.0 m and exerts
an average force of 190 N?
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W=Fxd
W = 190 N x 2.0 m
= 380 N●m = 380 J
Practice problems
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A mover is moving about 200 boxes a day.
How much work is he doing with each box,
assuming he lifts each 10 m with a force of
250 N.
Practice problems
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A mover is moves about 200 boxes a day.
How much work is he doing with each box,
assuming he lifts each 10 m with a force of
250 N.
Help
W=Fxd
= 250 N x 10 m
= 2,500 N●m = 2,500 J
Practice problems
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A box with a mass of 3.2 kg is pushed 0.667
m across a floor with an acceleration of 3.2
m/s2. How much work is done on the box?
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What do you need to calculate first?????
Practice problems
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A box with a mass of 3.2 kg is pushed 0.667
m across a floor with an acceleration of 3.2
m/s2. How much work is done on the box?
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F = ma
= 3.2 kg x 3.2 m/s2
= 10.2 kg● m/s2 = 10.2 N
Practice problems
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A box with a mass of 3.2 kg is pushed 0.667
m across a floor with an acceleration of 3.2
m/s2. How much work is done on the box?
F = ma
= 3.2 kg x 3.2 m/s2
= 10.2 kg● m/s2 = 10.2 N
W=Fxd
= 10.2 N x 0.667 m
= 6.80 N●m = 6.80 J
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• Practice problems
Get a calculator
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• Page 54 asks for distance……
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W= F x D
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• #1
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.6 m
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• #2
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.6m
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• #3
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2.6m
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• #4
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2.398m
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• P55 asks for force
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W= F x D
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• #5
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2 800 000N
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• #6
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27N
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• #7
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900 000N
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• #8
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95 454N
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• P56 asks for W………thank goodness
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W= F x D
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• #9
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237 825J
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• #10
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3.2 x 106 J
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• #11
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5 625 000 J
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• #12
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2 127 840J
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How about a harder one….
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#18
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• #18
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• Calculate force first, then work
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276 115J
Power
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• Power is a quantity that measures the rate
at which work is done
– It is the relationship between work and time
– If two objects do the same amount of work, but
one does it in less time. The faster one has
more power.
• Rate at which work is done or how much
work is done in a certain amount of time
Power
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• Formula for power:
Power = work
time
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P = W/t
• SI units for power – watts (W)
• 1 kW – Kilowatt = 1000 watts
• 1 MW – Megawatt= 1 million watts
Power
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• A watt is the amount of power required to
do 1 J of work in 1 s. (Reference – the
power you need to lift an apple over your
head in 1 s)
• Named for James Watt who developed the
steam engine in the 18th century.
Practice problems
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A weight lifter does 686 J of work on a weight
that he lifts in 3.1 seconds. What is the
power with which he lifts the weight?
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P = W/t
Practice problems
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A weight lifter does 686 J of work on a weight
that he lifts in 3.1 seconds. What is the
power with which he lifts the weight?
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P = W = 686 J
t
3.1 s
221 J/s = 221 W
Practice problems
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• How much energy is wasted by a 60 W bulb
if the bulb is left on over an 8 hours night?
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P=W
t
Practice problems
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• How much energy is wasted by a 60 W bulb
if the bulb is left on over an 8 hours night?
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P=W
t
1st convert 8 hr to seconds
8 hr (60 min/1hr)(60 sec/1min) = 28800 sec
Practice problems
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• How much energy is wasted by a 60 W bulb if the
bulb is left on over an 8 hours night?
P=W
t
1st convert 8 hr to seconds
8 hr (60 min/1hr)(60 sec/1min) = 28800 sec
2nd calculate for energy
W=Pxt
= 60 W x 28800 sec
= 1.7 x 107 J
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• Practice problems
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• P58 asks for work
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P= W/t
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• #1
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412.5J
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• #2
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1 710 000J
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• #3
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7 500 000 J
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• #4
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1.17 x 1010J
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• P59 asks for time
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• #5
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955.36 sec
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• #6
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456.14sec
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• #7
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1 500sec
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• #8
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4.5sec
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• P60 asks for power
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• #9
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5 x 108 watts
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• #10
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2.75 x 1010
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• Do 11 & 12
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• #11
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300sec
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• #12
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6 162 000J
Machines and Mechanical Advantage
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• Which is easier… lifting a car yourself or
using a jack?
• Which requires more work?
• Using a jack may be easier but does not
require less work.
– It does allow you to apply less force at any
given moment.
What is a machine?
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• A device that makes doing work easier… is
a machine
• Machines increase the applied force and/or
change the distance/direction of the applied
force to make the work easier
• They can only use what you provide!
Why use machines?
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• If machines cannot make work, why
use them?
– Same amount of work can be done by
applying a small force over a long
distance as opposed to a large force over
a small distance.
Effort and Resistance
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• Machines help move things that resist
being moved
• Force applied to the machine is effort
force (aka: Input force)
• Force applied by the machine is
resistance force (aka: Load, output
force)
Mechanical Advantage
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• Mechanical advantage is a quantity that
measures how much a machine multiplies
force or distance
• Defined as the ratio between output force
and input force
Mechanical Advantage
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• Mechanical advantage = output force
input force
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• Mechanical advantage= input distance
output distance
Machines
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Simple Machines
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
Lever
 Pulley
 Wheel & Axle

Inclined Plane
 Screw
 Wedge
The Lever family
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• Lever
– a rigid bar that is free to pivot about a fixed
point, or fulcrum
– Force is transferred from one part of the arm
to another.
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Resistance
arm
Effort arm
Fulcrum
Engraving from Mechanics Magazine, London, 1824
“Give me a place to stand and I will move the Earth.”
– Archimedes
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Lever
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•
First Class Lever
–
–
–
–
Most common type
Fulcrum in middle
can increase force, distance, or neither
changes direction of force
Lever
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•
Second Class Lever
– always increases force
– Resistance/load in middle
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Lever
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• Third Class Levers
– always increases distance
– Effort in middle
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Pulley
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• Pulley
– grooved wheel with a rope or chain running
along the groove
– a “flexible first-class lever” or modified lever
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F
Le
Lr
Pulley
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•
Ideal Mechanical Advantage (IMA)
– equal to the number of supporting ropes
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IMA = 0
IMA = 1
IMA = 2
Pulley
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• Fixed Pulley
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
IMA = 1

does not
increase
force

changes
direction of
force
Pulley
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• Movable Pulley
IMA = 2
 increases force
 doesn’t change direction

Pulley
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• Block & Tackle

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
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
combination of fixed & movable pulleys
increases force (IMA = 4)
may or may not change direction
Wheel and Axle
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• Wheel and Axle
– two wheels of different sizes that rotate
together
– a pair of
“rotating
levers”
– When the
wheel is turned
so is the axle
Wheel
so
Axle
Wheel and Axle
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• Wheel and Axle
– Bigger the difference in size between the
two wheels= greater MA
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Wheel
Axle
What is an inclined plane?
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• A sloping surface, such
as a ramp.
• An inclined plane can
be used to alter the
effort and distance
involved in doing work,
such as lifting loads.
• The trade-off is that an
object must be moved
a longer distance than
if it was lifted straight
up, but less force is
needed.
What is an inclined plane?
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• MA=Length/Height
Incline Plane Family
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• A wedge is a modified incline plane
– Example ax blade for splitting wood
– It turns a downward force into two forces
directed out to the sides
Incline Plane Family
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• A screw looks like a spiral incline plane.
– It is actually an incline plane wrapped around a
cylinder
– Examples include a spiral staircase and jar lids
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Practice problems
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• A roofer needs to get a stack of shingles
onto a roof. Pulling the shingles up
manually used 1549 N of force. Using a
system of pulleys requires 446 N. What is
the mechanical advantage?
Mechanical advantage = output force
input force
Practice problems
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• A roofer needs to get a stack of shingles onto a
roof. Pulling the shingles up manually used 1549 N
of force. Using a system of pulleys requires 446 N.
What is the mechanical advantage?
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Mechanical advantage = output force
input force
= 1549 N = 3.47
446 N
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•
Practice problems
1) Asks for output force (N)
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2) Asks for input distance (cm)
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3) Asks for output force (N)
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• #1
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444.4N
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• #2
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11cm
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• #3
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3 675N
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4) Asks for output distance (cm)
5) Asks for input force (N)
6) Asks for output distance (m)
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• #4
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3/0.85= 3.52
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• #5
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2220/.0893= 24 860N
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• #6
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1.57/12.5=0.1256m
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Solve for MA in #7 & #8
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• #7
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3.28
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• #8
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23.99
Compound Machines
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• Compound machines are machines made of
more than one simple machine
– Example include a pair of scissors has 2 first
class levers joined with a common fulcrum; each
lever arm has a wedge that cuts into the paper
Energy
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• Energy is the ability to cause changes.
– It is measured in Joules or kg●m/s2
– When work is done on an object, energy
is given off
Energy
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5 main forms of energy:
1. Mechanical – associated with motion
2. Heat – internal motion of atoms
3. Chemical – the energy required to bond atoms
together
4. Electromagnetic – movement of electric
charges
5. Nuclear – released when nuclei of atoms fuse
or split
Mechanical Energy
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• Mechanical Energy is the sum of the kinetic
and potential energy of a large-scale
objects in a system
– Nonmechanical energy is the energy that lies at
the level of atoms and does not affect motion
on a large scale
Energy
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• Those 5 forms of energy can be
classified into one of two states:
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– Potential energy – stored energy
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– Kinetic energy – energy in motion
Kinetic Energy
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• The energy of motion
• An object must have mass and be moving
to possess kinetic energy
– The greater the mass or velocity--- the greater
the kinetic energy
– Formula:
KE = ½ mv2
m = mass
v = velocity
Kinetic Energy
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• Atoms and molecules are in constant
motion and therefore have kinetic energy
– As they collide then the kinetic energy is
transferred from one to another
Practice problem
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A sprinter runs at a forward velocity of 10.9
m/s. If the sprinter has a mass of 72.5 kg.
What is their kinetic energy?
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KE = ½ mv2
Practice problem
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A sprinter runs at a forward velocity of 10.9
m/s. If the sprinter has a mass of 72.5 kg.
What is their kinetic energy?
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KE = ½ mv2
=
½ (72.5 kg) (10.9 m/s)2
= .5 x 72.5 x 118.81
= 4306.86 kg●m/s = 4306.86 J
Potential Energy
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• The stored energy that a body possesses
because of its position.
– Examples: chemical energy in fuel or food or an
elevated book because it has the potential to
fall.
• Potential energy due to elevated potential is
called gravitational potential energy (GPE).
Potential energy
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• Formula:
• PE = mgh
m = mass
g = gravity (9.8 m/s2)
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h = height
Practice problems
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A pear is hanging from a pear tree. The pear
is 3.5 m above the ground and has a mass
of 0.14 kg. What is the pear’s gravitational
potential energy?
Help
PE = mgh
Practice problems
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A pear is hanging from a pear tree. The pear
is 3.5 m above the ground and has a mass
of 0.14 kg. What is the pear’s gravitational
potential energy?
Help
PE = mgh
= .14 kg x 9.8 m/s2 x 3.5 m
= 4.8 kg●m2/s2 = 4.8 J
Conservation of Energy
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• Energy is almost always converted
into another form of energy
• One most common conversion is
changing from potential energy to
kinetic energy or the reverse.
Conservation of Energy
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• The transfer of energy from one object to
the next is a conversion of energy.
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The law of conservation of energy
states that all energy can neither
be created or destroyed; it is just
converted into another form.
Conservation of Energy
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• Energy conversions occur without a loss or
gain in energy
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• Therefore…. KE = PE
Energy Transformations
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Conservation of Energy
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• Amount of energy the machines transfers to
the object cannot be greater than energy
you put in
• Some energy is change to heat by friction
• An ideal machine would have no friction so
energy in = energy out
Efficiency
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• Efficiency is a measure of how much
work put into a machine is changed to
useful work output by the machine
• Not all work done by a machine is
useful therefore we look at the
efficiency of the machine
Efficiency
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• Formula for Efficiency
• (Work output / Work input) X 100
– Efficiency = useful work output x 100
work input
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• Efficiency is always less than 100% because no
machine has zero friction or 100% efficiency
• Lubricants can make a machine more efficient by
reducing friction
– Oil
– Grease
Practice Problem
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What is the efficiency of a machine if 55.3 J of
work are done on the machine, but only
14.3 J of work are done by the machine?
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Efficiency = useful work output
work input
Practice Problem
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What is the efficiency of a machine if 55.3 J of
work are done on the machine, but only
14.3 J of work are done by the machine?
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Efficiency = useful work output
work input
= 14.3 J x 100 = 25.9 %
55.3 J
Perpetual Motion Machines
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• Perpetual motions machines are machines
designed to keep going forever without any
input of energy
• It is not possible because we have not been
able to have a machine with a complete
absence of friction!
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• Newman’s machine
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Joseph Newman, claimed it
would produce mechanical
power exceeding the
electrical power being
supplied to it
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• Take out your homework
Power, Work and Force I
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1.
6.48W
7.
9.45W
2.
6 692J
8.
1.8kg
3.
5.76S
9.
61.25W
4.
112.93 kg
10.
11 340J
11.
4344.6W
5.
6.
7.11W
16.4S
Work and Power I
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1.
20J
10.
60W
2.
5 900J
11.
588W
3.
14 000J
12.
5000W
4.
50m
13.
115N in 15m(1725J
14.
20kg lift=1960J
5.
6.
5.10m
50W
15.
80%
7. 13W
16. 500J
8. 18 000J
17. over 490J
9. 100J
18. What do you think?
19. 25%