Download Chapter 10: Energy, Work and Simple Machines

Energy, Work and Simple
Machines
Chapter
Physics
Work
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Work has its own meaning in physics.
Work is done on an object when an applied force acting on the
object moves the object over a distance.
Work is a scalar, but it can be negative.
Work depends on two factors.
 Force (F)
 Displacement (d)
Work
Work = Force x Displacement
W = Fd
Unit for Work = Newton Meter (Nm)
1 Nm = 1 Joule (J) (Same as Energy)
Work is a scalar quantity (no direction)
In doing Work the Displacement has to be in the same direction as
the Force!
Work, Force and Direction
W = Fd
In doing Work the Displacement has to be in the same direction as
the Force!
If the Force is at an angle, then the component of the Force (Fx)
produces Work
W = Fxd = Fdcosq
Work
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Work can be Zero (WNET = 0) in three ways;
d = 0 (does not move or finishes where it starts)
FNET = 0 (v = 0 or v = constant)
FNET is perpendicular to d (F | d)
Work
If F ll d, then W = Fd or W = -Fd
W = Fd, Force in same direction as
displacement
(q = 0o:
cosq = 1, Positive Work)
W = -Fd, Force is in the opposite direction as
the displacement
(q =
180o: cosq = -1, Negative Work)
Negative Work
• When a force is applied and it goes against the displacement then we
call it negative work.
• Example : a car skidding to a stop on a roadway surface or a baseball
runner sliding to a stop on the infield dirt. In such instances, the force
acts in the direction opposite the objects motion in order to slow it
down. The force doesn't cause the displacement but rather hinders it.
These situations involve what is commonly called negative work
Work From a Force vs Displacement Graph
If you have a Force vs Displacement Graph, where the Force is in
Newtons (N) and the Displacement is in Meters (m), you can find the
Work by finding the Area Under the Curve!
W = Area under F vs d graph
Work From a Force vs Displacement Graph
W = Area under F vs d graph
For a Constant Force:
The Area is a rectangle use W = A = lw
For a Force Varying at a Constant Rate:
The Area is a triangle use W = A = ½ bh
Energy
Energy is the property that describes an object’s ability to change itself or
the environment around it.
Energy can be found in many forms.
Kinetic Energy (KE) – energy of motion.
Potential Energy (PE) – energy gained by a change in position or structure
Different Types of Energy
Electrical - energy from moving electrons
Gravitational energy – Energy due to change in position and gravity
Kinetic Energy – Energy of a moving object
Chemical Potential Energy – Energy stored within bonds
Elastic Potential Energy – Energy stored in a stretched objected
Nuclear Energy – Energy stored in the nucleus of the atom
Thermal Energy – Heat Energy (Energy due to the vibration of
molecules)
Kinetic Energy (KE)
Moving objects possess Kinetic Energy.
KE = ½ mv2
Energy is a scalar quantity and has the unit of Joule (J) (1 J = 1 Nm)
Nuclear Energy
• E=mc2
• E = Nuclear Energy (Joules)
• m= mass in kg
• c= speed of light (3x108m/s in a vacuum)
Elastic Potential Energy
• PE =1/2 kx2
• PE = Potential Energy (Joules)
• K = Spring constant (N/m)
• X = displacement (m)
Gravitational Potential Energy
Anything that can fall has GPE.
GPE =mgh
What is the gravitational potential energy of a dancer who has a mass
of 50kg and is 2m above the ground?
GPE=(50kg)(9.8)(2m) = 980J
Transforming Energy
• Due to the law of conservation of energy we can transform or
convert energy from one form to another.
• For instance in your car engine gasoline, which is chemical potential
energy is converted into thermal (heat), sound, and kinetic energy. A
more efficient engine is going to convert more of the chemical
energy into kinetic energy and less into sound and thermal energy.
That is why modern engines are more efficient than the old engines.
Conversions between Kinetic and Potential
Energy
• We encounter many situations where we have convert potential
energy to kinetic, can you demonstrate some?....
• If an object is being dropped, GPE=KE + GPE until the object hits the
ground.
• Therefore At the top or bottom of a drop/ramp use :
• GPE TOP= KEBottom
•
In the middle of a drop/ ramp use :
• GPETOP=ke +gpe
KEBOTTOM= ke + gpe
OR
Mechanical Energy
• Mechanical energy is the total amount of potential energy and
kinetic energy in a system and can be expressed by this equation.
• Mechanical energy = potential energy + kinetic energy
Work-Energy Theorem
Work and Energy are closely related.
Work and Kinetic Energy can be connected with the kinematics
equations and Newton’s 2nd Law
W = DKE (Work-Energy Theorem)
W = KEf – KEi = ½ mvf2 – ½ mvi2
If something is being lifted :
W = GPEf – GPEi = mghf-mghi= mg(∆h)
Solving Conservation of Energy Problems on a
ramp/drop
• Steps :
1- Ask yourself, where are you in the drop or ramp. Are you at the
bottom or top, or are you somewhere else!
2- If you are at the top or bottom then GPE TOP= KEBottom
3. If you are somewhere else then use GPETOP=ke +gpe
OR
KEBOTTOM= ke + gpe
4. Then substitute in the values that you are given in the problem. You
may use gpe=mgh and ke=1/2mv2 here
5.Solve for what you are asked to solve for.
Power
Power – The time rate of doing Work
If you do the same Work faster, you have more Power!
Power = Work/Time
P = W/Dt
Unit for Power = J/s
1 J/s = 1Watt (W)
Power
Power is a scalar quantity (no direction)
Another way to find Power:
P = W/t = (Fd)/t
Since v = d/t
P = Fv = Force x Velocity = Power
Since a Watt is small, Power often uses
kilowatt (kW) megawatt (MW) or
Horsepower (hp)
Energy From Power
We can use the Power Equation to find Energy.
P = W/t (Work is similar to Energy)
Therefore; P = E/t
E = Pt
(Solve for Energy)
A Unit for Energy = W s or kW-hr (kilowatt-hour)
Machines
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Machines can do any of the following;
Machines can Multiply the Force (Lever)
Change the Direction of the Force (Pulley)
Change the speed in which the force acts (Gears)
Machines
Most machines make work easier by multiplying the Force!
Machines never Multiply the Work!
When using a machine there is always a Work put into the machine
(WIN) and a Work the machine puts out (WOUT).
Ideally, the WIN = WOUT in an ideal machine (no friction).
Machines
How Does a Machine multiply the force without multiplying the
Work?
Answer: If a machine multiplies the Input Force (FIN), then the
machine must act over a larger Displacement (dIN)!
 Remember, W = Fd
Machines
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WIN = WOUT
FIN dIN = FOUT dOUT
FIN will be small so dIN will be large!
FOUT will be large so dOUT will be small!
Types of Simple Machines
 Simple Machine (SM) – a machine with one
or two moving parts.
 There are six types of Simple Machines:
 1. Lever
4. Inclined Plane
 2. Pulley
5. Wedge
 3. Wheel and
6. Screw
Axle
Mechanical Advantage
Mechanical Advantage (MA) – is the number of times a machine
multiplies the Input Force (FIN)
Example:
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MA = 2 Means the machine doubles the force you put into it.
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MA = 10 Means the machine multiplies the force put into it by
10.
Mechanical Advantage
MA >1 (Machine multiplies the force)
MA < 1(Machine multiplies the distance)
MA = 1(Machine does not multiply either force or distance.
Probably only changes the direction to the force.)
Mechanical Advantage
To find the Mechanical Advantage (MA) of a machine, we take the
ratio of the Resistance Force (Fr) to the Effort Force (Fe)
MA = Fr/ Fe
Effort Force (Fe) – is the force applied to the machine
Resistance Force (Fr) – is the force the machine applies to the object
Ideal Mechanical Advantage (IMA)
The Ideal Mechanical Advantage (IMA) is the largest possible MA a
machine can have if the machine operated without friction.
To find the Ideal Mechanical Advantage (IMA) of a machine you
take the ratio of the Effort Distance (de) over the Resistance Distance
(dr)
Calculating MA and IMA
To calculate MA we use the Forces (Fr and Fe). Since Friction is a
force, Friction affects MA. MA = Fr/Fe
To calculate IMA we use the distances (dr and de). Friction does not
affect IMA. IMA = de/dr
MA has No Unit!! It’s a number telling how many times the force is
multiplied!
Ideal Mechanical Advantage and Actual
Mechanical Advantage
The Actual Mechanical Advantage (MA) is always less than the IMA
(MA < IMA) because of Friction.
Machines are designed with an IMA
Machines are tested to find Actual MA
Input/Effort and Output/Resistance
Note from this point on:
Effort = Input
(FIN = Fe and dIN = de)
Resistance = Output
(FOUT = Fr and dOUT = dr)
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WIN = WOUT (Ideal Machine)
Fede = Frdr
Compound Machines
Compound Machine – any combination of two or more simple
machines
Examples: Axe, Shovel, Scissors
Compound Machines have a higher Mechanical Advantage (MA)
because they are made up of multiple machines
Mechanical Advantage of Compound
Machines
To calculate the Mechanical Advantage (MA) of a Compound
Machine (CM), you multiply the Mechanical Advantages of all the
Simple Machines in the Compound Machine
MACM = MASM#1 x MASM#2 x MASM#3 x …
Efficiency
Efficiency is the ratio of the useful work you get out of a machine
(WOUT) over the work you put into a machine (WIN)
In an ideal world (no friction);
WOUT = WIN therefore;
WOUT/WIN = 1
Efficiency
In the real world (with friction);
WOUT < WIN therefore;
WOUT/WIN < 1
We express Efficiency as a Percentage by multiplying the ratio by
100%
Ideal World Efficiency = 100%
Real World Efficiency < 100%
Efficiency
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We can use different equations for Efficiency
Eff = (WOUT/WIN) x 100%
Eff = (Frdr/Fede) x 100%
Eff = (MA/IMA) x 100%
Efficiency and Machines
Simple Machines have a small MA but work with a high Efficiency.
Compound Machines have a high MA but work with a lower
Efficiency.
The more complicated the machines the greater the MA but the
lower the Efficiency!
The Human Machine
Levers – Muscles and Tendons
Wedges – Teeth and Finger Nails
Your Body uses many Simple and Compound machines to create
Mechanical Advantage
Human Walking Machine
Machine – a device that makes
doing work easier by…
increasing the force that can be
applied to an object. (car jack)
 increasing the
distance over which
the force can be
applied. (ramp)
by changing the direction of
the applied force. (opening the
blinds)
A. Lever
• Lever
• a bar that is free to pivot about a fixed point, or fulcrum.
Resistance
(output)
Arm
Work is
done here.
Effort
(input) arm
You apply
your force
Fulcrum
Engraving from Mechanics Magazine, London, 1824
“Give me a place to stand and I will move the Earth.”
– Archimedes
First Class Lever
• First Class Lever
• the fulcrum is in the middle
• changes direction of force
• Ex: pliers, seesaw
Second Class Lever
• Second Class Lever
• The output (resistance) is in the middle
• always increases force
• Ex: wheelbarrow, nutcracker
Third Class Lever
• Third Class Levers
• Input (effort) force is in the middle
• always increases distance
• Ex: tweezers, bat, human body
Think FOIL
•Fulcrum in middle = 1st class lever
•Output in middle = 2nd class lever
•Input in middle = 3rd class lever
•LEVERS
B. Pulley
• Pulley
• grooved wheel with a rope or chain running along the groove
• a “flexible first-class lever”
F
Le
Lr
B. Pulley
• Ideal Mechanical Advantage (IMA)
• equal to the number of rope segments if pulling up
• Equal to one less than the number of rope segments (minus
1) if pulling down.
IMA = 0
IMA = 1
IMA = 2
B. Pulley
• Fixed Pulley
– IMA = 1
– does not increase
force
– changes direction
of force
B. Pulley
• Movable Pulley
– IMA = 2
– increases force
– doesn’t change direction
B. Pulley
• Block & Tackle
– combination of fixed & movable pulleys
– increases force (IMA = 4)
– may or may not change direction
C. Wheel and Axle
• Wheel and Axle
• two wheels of different sizes that rotate together
• a pair of “rotating
levers”
• effort force is applied to
wheel
• axle moves less
distance but with
Wheel
greater force
Axle
D. Inclined Plane
• Inclined Plane
• sloping surface used to raise objects
• Ramps, mountain roads
l
h
E. Screw
• Screw
• inclined plane wrapped in a spiral around a cylinder
F. Wedge
• Wedge
• a moving inclined plane with 1 or 2 sloping sides
F. Wedge
• Zipper
• 2 lower wedges push teeth together
• 1 upper wedge pushes teeth apart
F. Wedges
How do machines make work easier?
• 1. Machines increase force (total distance traveled is greater)
• 2. Machines increase distance (a greater force is required
• 3. Changes direction
Machines
IV. Using Machines
Compound Machines
 Efficiency
 Mechanical Advantage

A. Compound Machines
• Compound Machine
• combination of 2 or more simple machines
A. Compound Machines
• Rube Goldberg Machine
A Rube Goldberg machine,
contraption, invention, device, or
apparatus is a deliberately overengineered or overdone machine
that performs a very simple task
in a very complex fashion, usually
including a chain reaction. The
expression is named after
American cartoonist and inventor
Rube Goldberg
Work In
Effort force – FE (Force in)
The force applied to the
machine (usually by you)
Work in – Win (Force in x distance in)
The work done by you on the
machine
Work Out
Resistance force – FR (Force out)
The force applied by the
machine to overcome resistance
Work out – Wout
(Force out x distance out)
The work done
by the machine
Mechanical Advantage
•Ideal Machine the Win = Wout
•100% energy transfer
•There is no such thing as an ideal machine –
you always lose some energy (through friction,
air resistance, etc.)
•Ideal mechanical advantage is how much a
machine multiplies force or distance without
friction.
Mechanical Advantage
•How much a machine multiplies force
or distance
output force (FR)
•MA = input force (FE)
Or
input distance
output distance
Mechanical Advantage
• The number of times a force exerted on a machine is
multiplied by the machine
• Mechanical advantage (MA) = resistance force
effort force
• Mechanical advantage (MA) = effort distance
resistance distance
Mechanical Advantage
What is the mechanical advantage of the following simple
machine?
3m
GIVEN:
WORK:
de = 12 m
dr = 3 m
MA = ?
MA =de ÷ dr
MA = (12 m) ÷ (3 m)
MA = 4
de
MA dr
Mechanical Advantage
Calculate the mechanical advantage of a ramp that is 6.0 m
long and 1.5 m high.
GIVEN:
WORK:
de = 6.0 m
dr = 1.5 m
MA = ?
MA =de ÷ dr
MA = (6.0 m) ÷ (1.5 m)
MA = 4
de
MA dr
D. Mechanical Advantage
• A worker applies an effort force of 20 N to open a window
with a resistance force of 500 N. What is the crowbar’s MA?
GIVEN:
WORK:
Fe = 20 N
Fr = 500 N
MA = ?
MA = Fr ÷ Fe
MA = (500 N) ÷ (20 N)
MA = 25
Fr
MA Fe
Mechanical Advantage
What is the mechanical advantage of the following simple
machine?
How much work did the
machine do?
GIVEN:
WORK:
Fe = 25 N
Fr = 500 N
MA = ?
MA =Fr ÷ Fe
MA = (500N) ÷ (25N)
MA = 20
Fr
MA Fe
Shortcut for finding M.A. of Pulleys
• Mechanical Advantage of pulleys is very easy
• Count the number of rope segments visible
• If rope is pulling down, subtract 1
• If rope is pulling up, do nothing
• Example:
• 5 rope segments
• Pulling down so subtract 1
• Mechanical Advantage = 5-1= 4
• Pulley A
• 2 rope segments
• Subtract 1 b/c pulling down
• MA = 2-1=1
• Pulley B
• 2 rope segments
• Pulling up do nothing
• MA=2
Pulley
Pulley
• A:
• B:
• C:
• D:
• E:
2-1=1
2
3-1=2
3
4-1=3
Ideal machine
Win = Wout
100% energy transfer.
There is no such thing as an ideal
machine – you always lose some
energy (through friction, air resistance,
etc.)
Efficiency – a measure of how
much of the work put into a
machine is changed into useful
output work by the machine.
(less heat from friction)
•efficiency =
(Wout / Win ) x 100%
•Win is always
greater than Wout
Efficiency
• Efficiency
• measure of how completely work input is converted to work output
Wout
Efficiency 
 100%
Win
– always less than 100% due to friction
Efficiency Practice Problems
• If a machine requires 26.0 J of work input to operate and produces
22.0 J of work output, what is its efficiency?