simple machines math (mechanical advantage, efficiency, and energy)
TRANSCRIPT
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Simple Simple MachinesMachines
MathMath(Mechanical Advantage, (Mechanical Advantage, Efficiency, and Energy)Efficiency, and Energy)
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What is an instrument that
makes work easier called?
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What is an instrument that
makes work easier called?
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What are the two types of work
involved in using a machine?
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What is an instrument that makes work easier
called?
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Describe the two types of
work involved in using a hammer.
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Describe the two types of
work involved in using scissors.
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Describe the two types of
work involved in using a rolling pin.
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Can a machine increase the work you
put into it?
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Can a machine increase the work you
put into it?
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Mechanical Mechanical AdvantageAdvantage
Mechanical Advantage – a quantity that measures how much a machine multiplies force or distance.
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Mechanical Mechanical AdvantageAdvantage
The mechanical advantage tells you how much the force will increase by using a particular machine. The more times a machine multiplies the input or effort force, the better the machine is.
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Mechanical Mechanical AdvantageAdvantage
When the mechanical advantage is greater than 1, the machine increases or multiplies the force you apply.
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Mechanical Mechanical AdvantageAdvantage
Machines do not increase the work you put into them.
The work that goes into a machine can never be greater than the work that comes out of the machine.
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Mechanical Mechanical Advantage EquationAdvantage Equation
mechanical advantage = output force = input distance input force output distance
M.A. = Fo = di
Fi do
mechanical advantage = resistance force = effort distance effort force resistance distance
M.A. = FR = dE
FE dR
The resistance force can be just the weight of the object you are trying to move. (Weight is a force of gravity.)
Mechanical advantage has no units.
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M.A. Problem 1M.A. Problem 1What is the mechanical advantage of a crowbar that allows you to put 25 newtons of force into lifting a 250 newton crate?
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M.A. Problem 1M.A. Problem 1What is the mechanical advantage of a crowbar that allows you to put 25 newtons of force into lifting a 250 newton crate?
M.A. = Fo Fi
M.A. = 250 N = 10 25 N
M.A. = FR FE
M.A. = 250 N = 10 25 N
How many times does the crowbar multiply the force that wasput into it? (Hint: Look at the answer.)
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M.A. Problem 2M.A. Problem 2What is the mechanical advantage of ramp that is 10 m long and 3 m high?
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M.A. Problem 2M.A. Problem 2What is the mechanical advantage of ramp that is 10 m long and 3 m high?
M.A. = di do
M.A. = 10 m = 3.3 3 m
M.A. = dE dR
M.A. = 10 m = 3.3 3 m
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M.A. Problem 3M.A. Problem 3A pulley system has a mechanical advantage of 10. a. If a mover uses this pulley to lift a piano with a weigh of 1450 N a distance of 4 m, how much force must the mover use?b. How far will the mover pull the rope?
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M.A. Problem 3M.A. Problem 3
a. M.A. = Fo Fi
10 = 1450 N Fi
Fi = 1450 N 10
Fi = 145 N
A pulley system has a mechanical advantage of 10. a. If a mover uses this pulley to lift a piano with a weigh of 1450 N a distance of 4 m, how much force must the mover use?b. How far will the mover pull the rope?
b. M.A. = di do
10 = di 4 m
(10)(4m) = di
di = 40 m
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Can the work that comes out of a
machine be greater than the work that goes
into the machine?
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Can the work that comes out of a machine be greater than the work that goes into the
machine?
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Are any actual actual machinesmachines
100% efficient?
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Are any actual machines 100% efficient?
There are no machines that are 100% efficient. Every machine deals with friction…some more than others. Friction is a force that opposes motion.
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Ideal MachinesIdeal Machines
Ideal Machines are 100% efficient.
Ideal Machines do not exist.
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What form of energy does friction produce?
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What form of energy does friction produce?
heat
Why? Friction opposes motion.
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EfficiencyEfficiencyThe efficiency of a machine is defined as the
ratio of the output work to the input work.
efficiency = work output x 100% work input
eff = Wo x 100% Wi
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EfficiencyEfficiencyIn an ideal machine…
- work output equals work input. - the efficiency is 100%.
In real machines… - the efficiency is less than 100%. - work output is less than work input. - loss due to friction and heat.
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Efficiency Problem 1Efficiency Problem 1 A man uses 419 J of work in removing a
nail from a piece of wood with a hammer. The hammer has a work output of 305 J. What is the efficiency of the hammer?
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Efficiency Problem 1Efficiency Problem 1 A man uses 419 J of work in removing a nail
from a piece of wood with a hammer. The hammer has a work output of 305 J. What is the efficiency of the hammer?
eff = Wo x 100% Wi
eff = 305 J x 100 419 J
eff = 72.8 %
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Efficiency Problem 2Efficiency Problem 2 John uses 39 J of energy to
move four boxes with the handcart. The work output from the handcart is 32.4 J. What is the efficiency of the handcart?
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Efficiency Problem 2Efficiency Problem 2 John uses 39 J of energy to move four
boxes with the handcart. The work output from the handcart is 32.4 J. What is the efficiency of the handcart?
eff = Wo x 100% Wi
eff = 32.4 J x 100 39 J
eff = 83 %
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Moment ProblemsMoment Problems
Moment = length mass
momentresistance = momenteffort
(length mass)resistance = (length mass)effort
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Moment ProblemsMoment Problems
45 g 22.3 g
resistance arm5 m
effort arm? m
Solve for the missing quantity.
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Moment ProblemsMoment Problems
(length mass)resistance = (length mass)effort
(45 g 5 m) = (22.3 g X)
X = 10.09 m
45 g 22.3 g
resistance arm5 m
effort arm? m
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Moment ProblemsMoment Problems
38 g 13.5 g
resistance arm3 m
effort arm? m
Solve for the missing quantity.
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Moment ProblemsMoment Problems
38 g 13.5 g
resistance arm3 m
effort arm? m
(length mass)resistance = (length mass)effort
(38 g 3 m) = (13.5 g X)
X = 8.4 m
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EnergyEnergy
Energy is the ability to do work.
Potential Energy – energy at rest due to position, composition, or compression.
Kinetic Energy – energy of motion
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Potential EnergyPotential Energypotential energy = mass free fall acceleration height
PE = m g h
J = kg m/sec2 m
1 joule = 1 kg m2
sec 2
g = 9.8 m/sec2
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Potential Energy Problem Potential Energy Problem 11
A rock climber climbs 63 m to the top of a cliff. If the rock climber has
a mass of 85 kg, what is the potential energy of the climber?
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Potential Energy Problem Potential Energy Problem 11
A rock climber climbs 63 m to the top of a cliff. If the rock climber has a mass of 85 kg, what is the potential energy of the climber?
PE = m g h
PE = (85 kg)(9.8 m/sec2)( 63 m)
PE = 52,479 J
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Potential Energy Problem Potential Energy Problem 22
A 1.8 kg book sits on top of a 2.8 m shelf. What is the potential energy of the book?
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Potential Energy Problem Potential Energy Problem 22
A 1.8 kg book sits on top of a 2.8 m shelf. What is the potential energy of
the book?
PE = m g h
PE = (1.8 kg)(9.8 m/sec2)( 2.8 m)
PE = 49.39 J
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Kinetic EnergyKinetic EnergyKinetic energy = ½ mass speed squared
KE = ½ m v2
J = ½ kg m2/sec2
1 joule = 1 kg m2
sec 2
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Kinetic Energy Problem 1Kinetic Energy Problem 1
What is the kinetic energy of a 35 kg dog running at 2.8 m/sec?
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Kinetic Energy Problem 1Kinetic Energy Problem 1
What is the kinetic energy of a 35 kg dog running at 2.8 m/sec?
KE = ½ m v2
KE = ½ 35 kg (2.8 m/sec)2
KE = 137.2 J
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Kinetic Energy Problem 2Kinetic Energy Problem 2
What is the kinetic energy of a 1635 kg car traveling at 29 m/sec?
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Kinetic Energy Problem 2Kinetic Energy Problem 2
What is the kinetic energy of a 1635 kg car traveling at 29 m/sec?
KE = ½ m v2
KE = ½ 1635 kg (29 m/sec)2
KE = 687,517.5 J