All about Simple Machines

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All about Simple Machines

• Simple machines are the basic building blocks for
  
• any mechanical device or complex machines.
• Simple machines are used to
• Transfer kinetic energy (the energy of motion)
• Reduce the effort needed to move a heavy load
• Change the direction or amount of motion
• Change the type of motion (rotary to straight
  line)

Final Copy Prepared by G. Reluzco
1.1.04
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• There are six Simple Machines
• Lever
• Wheel Axle
• Pulley
• Inclined Plane
• Wedge
• Screw

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Simple Machines- Key Terms and Symbols
Effort (E) is the input force which must be
supplied by the user or an engine of some
kind. Load (R) is the output force which is also
the force resisting motion. Mechanical
Advantage (MA) is a measure of how much the
effort is decreased by the simple machine. It is
defined as Mechanical Advantage Load
or MA R Effort E
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Simple Machines- Key Terms and Symbols
Mechanical Advantage as defined by the ratio of
forces is also referred to as Actual Mechanical
Advantage because it can be directly
measured. Mechanical Advantage can also be
defined by the geometry or dimensions of the
various simple machines. This method is referred
to as Ideal Mechanical Advantage because it
does not include the effects of friction. Actual
and Ideal Mechanical Advantage are equal if the
friction is zero (practically not possible in the
real world)
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Simple Machines- Key Terms and Symbols
In physics Work is defined as the force applied
on an object times the distance traveled by the
object.
Initial position
Final position
Force (F)
Distance (d)
Work Force Distance Fd
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Simple Machines- Key Terms and Symbols
Simple machines are used to do work by applying
an effort to move a load. The amount of work done
is the same regardless of how much mechanical
advantage a simple machine provides. In other
words the product of the effort times the
distance traveled will be the same no matter how
much mechanical advantage you get from the simple
machine.
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Levers
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Lever The lever is a rigid bar which pivots at a
point called the fulcrum. The forces on the lever
are the Effort (E) and the load (R).
E
R
Fulcrum
In order for the lever to be balanced or in
equilibrium, the turning effect of each force
must be equal. The turning effect of a force is
called a Moment or Torque.
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Lever The moment is defined by Moment Force
x distance to fulcrum Note the distance must be
measured perpendicular to the direction of the
force. Moments or torques can be () or (-) and
are shown as
CW (-)
CCW ()
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Example of a lever in equilibrium
1200 lbs
300 lbs
4 feet
1 foot
Moment 1 Moment 2 Force 1 x distance 1 Force
2 x distance 2 300 x 4 1200 x 1 1200 ft-lb
1200 ft-lb Equal moments are required for
equilibrium
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Lever Mechanical Advantage For the previous
example Mechanical Advantage Load
Effort MA R 1200 4 E
300 Notice that you can also calculate MA from
the ratio of the lengths from the fulcrum to the
force MA Length to Effort LE 4 4
Length to Load LR 1
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Lever In general terms the lever can be
described as
R
E
LE
LR
Where E Effort R Load LE distance from
fulcrum to Effort LR distance from fulcrum to
Load
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Important Formula for All Simple Machines
Mechanical Advantage Load
Effort or
MA R
E
(Eq. 1)
This is a key formula which will be used on all
the simple machines. The definition of Mechanical
Advantage will change from one simple machine to
the next.
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Important Formulas for Levers
For a lever the following formulas can also be
used Mechanical Advantage Length to Effort
Length to
Load MA LE
LR Or you can
also use the moment equilibrium formula (its the
same equation arranged differently)
LE E LR R
(Eq. 2)
(Eq. 3)
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Lever Q Suppose you were given a 6 board and a
log to use as a fulcrum and you wanted to lift a
heavy object a short distance. Where would you
place the log?
Q Why?
A Locate the log as close as possible to the
load. This will maximize the mechanical
advantage. LE becomes very large. LR becomes very
small. MA increases.
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Types of Levers 1st Class Lever- Fulcrum is
between the Load and Effort.
R
E
1st Class levers can have a mechanical advantage
greater than or less than one depending on the
values of LE and LR. If LE gt LR then MA gt1.
Example A pair of pliers If LEltLR then MAlt1.
Example Salad Tongs
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2nd Class Lever- Load is between the Fulcrum and
Effort.
R
E
2nd Class levers must have a mechanical advantage
greater than one because LE is larger than
LR. If LE gt LR then MA gt1. Example A
wheelbarrow
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3rd Class Lever- Effort is between the Fulcrum
and Load.
R
E
3rd Class levers must have a mechanical advantage
less than one because LR is larger than LE. If
LE lt LR then MA lt1. Example A shovel
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1st Class Lever Examples
2nd Class Lever Examples
3rd Class Lever Examples
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Mechanical Advantage is not free! You must pay a
price when the mechanical advantage is greater
than one. The price you pay is you must travel a
longer distance. If you are using a claw hammer
to remove a nail think of the distance your hand
travels compared to the distance the nailhead
moves.
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R
E
Examples
LE
LR

• Given LR 2 , LE 6 , E 1 lb.
  Unknown R ?
• Solve Equation (3) for R.
• R LE / LR E 6 / 2 1 3 lbs
• Another approach to the same problem is
• Solve Equation (1) for R. Then substitute
  Equation (2).
• R MA E LE / LR E 6 / 2 1 3
  lbs
• Given R 8 lbs , LE 4 , E 4 lb.
  Unknown LR ?
• Solve Equation (3) for LR.
• LR LE E / R 4 4 / 8 2

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Wheel and Axle A wheel axle is used to change
the amount of force transferred or to change from
rotary motion to linear (straight line) motion.
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Wheel and Axle The wheel and axle can be made by
rotating a lever around the pivot point. Start
with a 2nd class lever.
Wheel
E
R
Axle
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Wheel and Axle Notice in this case the effort is
applied at the wheel and the resistance at the
axle. Is MA greater or less than 1? An
example of this is the steering wheel on a car.
The drivers hands supply the effort, the steering
mechanism provides the load. The larger the wheel
diameter, the greater the MA and the easier it is
to turn the wheel. The hands have to travel a
longer distance as the wheel gets larger.
Greater than 1 because LE gt LR
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Wheel and Axle Now start with a 3rd class lever
and rotate about the fulcrum.
Wheel
E
R
Axle
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Wheel and Axle Notice in this case the effort is
applied at the axle and the resistance at the
wheel. Is MA greater or less than 1? An example
of this is the drive axle on a car. The engine
supplies the effort on the axle, the friction of
the tires contacting the road provide the load.
The larger the wheel diameter, the lower the MA
and the more difficult it is for the engine to
turn the wheel. You do increase the speed of the
car though.
Less than 1 because LE lt LR
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Important Formulas for Wheel Axle
Mechanical Advantage Load R
Effort E And
MA Radius to Effort LE
Radius to Load LR
(Eq. 4)
(Eq. 5)
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Examples

• Given a wheel used to turn a valve stem on a
  water valve.
• Wheel Radius 12 Axle Radius 0.5
• What is the Mechanical Advantage?
• Solve Eq. (5). MA wheel radius 12 24
• axle radius
  0.5
• Given a wheel and axle used to drive the wheels
  of a car.
• Wheel radius 15 Axle Radius 1
• What is the mechanical advantage?
• Solve Eq. (5). MA axle radius 1 0.066
• wheel radius

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Wheel Axle The Wheel Axle can be used to
convert rotary motion to linear motion. Consider
a wheel axle rolling on the ground. As the
wheel turns the wheel axle travel in a straight
line (linear motion), the distance traveled in
one revolution of the wheel is
S
S Distance traveled in one revolution S
Circumference of wheel S Pi Wheel Diameter S
3.141 D
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Wheel Axle Q You have the choice of putting a
26 diameter tire or a 30 diameter tire on your
bicycle? Which tire will increase the top speed
of the bike? How much will the speed change in
percent? A The larger the tire diameter the
greater the linear distance traveled (S) for one
revolution of the wheel. S 3.141 26
81.666 in distance for 26 dia. Tire S
3.141 30 94.23 in distance for
30 dia. Tire Linear speed distance / time
if the distance increases the speed also
increases Change (94.23- 81.666) 100
15.4 speed increase
81.666
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• Pulleys
• The pulley is an adaptation of the wheel axle.
• Pulleys can be used to
• change the direction of motion.
• reduce the effort required to move a load.

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Pulleys As the mechanical advantage of the
pulley increases larger loads can be moved. The
trade off is the end of the rope must travel a
longer distance than the load. The amount of
work done at each end of the pulley system is the
same. Work at Effort end Work at Load
end Effort distance traveled by rope Load
distance moved by Load
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Important Formulas for the Pulley
Mechanical Advantage Load R
Effort E and MA
the number of strands supporting the load. Note
This method of determining MA is only valid when
you have one continuous rope in the pulley system.
(Eq. 6)
(Eq. 7)
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Pulleys Look at 3 types of pulleys. For
Mechanical Advantage count the end strand only
when the effort is pointed upwards.
 
Fixed Pulley
Movable Pulley
Block Tackle
E
E
E
 
MA 1
MA 2
MA 3
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Pulleys
Fixed Pulley is attached or fixed to a stationary
object. MA 1. The effort and load are equal. If
the load is lifted 1 the rope is pulled 1.
Movable Pulley is attached to the moving load.
MA 2. The effort is half the load. If the load
is lifted 1 the rope is pulled 2. Block
Tackle is a system of 3 pulleys. MA 3. The
effort is one third the load. If the load is
lifted 1 the rope is pulled 3.
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Pulley Example The pulley system shown below is
used to lift a load of 60 lbs a distance of 2.
How much effort must be applied and how much rope
do you need to pull?
MA 6 Solve Eq(6) for the Effort Effort Load /
MA 60 / 6 Effort 10 lbs Distance traveled
2 6 Distance traveled 12
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Inclined Plane
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Inclined Plane- Examples
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Inclined Plane Inclined Plane is a flat sloped
surface that can be used to reduce the amount of
effort required to lift a load. The inclined
plane makes an angle theta with the ground ( a
horizontal line). A load R is being raised from
point A to point B. The height from A to B is H.
The length of the inclined surface is L. The
effort, E, is applied in a direction parallel to
the inclined surface. The incline make an angle
theta, ?, with the horizontal.
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Inclined Plane- Geometry and Definitions
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Important Formulas for the Inclined Plane
Mechanical Advantage Load R
Effort E and MA
L H Note Equation 9 is only valid if
you assume there is no friction. It is the ideal
mechanical advantage.
(Eq. 8)
(Eq. 9)
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Inclined Plane Ex Given the inclined plane
geometry, and the effort find the mechanical
advantage and the maximum load that can be moved.
What is the tradeoff for reducing the
effort? Given L 12 , H 3, E 30 lbs.
Find MA and R. Equation MA L/H 12/3
4 R MA E 4 30 120 lbs The price paid
for mechanical advantage is the object travels
12 along the incline to increase the height by
3.
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Wedge
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Wedge- Examples
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Wedge The wedge is a modification of the
inclined plane. Wedges are used to separate or
hold devices. There are two major differences
between inclined planes and wedges. During use an
inclined plane remains stationary while the wedge
moves. With an inclined plane the effort force is
applied parallel to the slope of the incline.
With a wedge the effort force is applied to the
vertical edge (height) incline.
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Wedge -Comparison to the Inclined Plane
Effort
Effort
Inclined Plane
Wedge
Wedges can be single or double
L
L
H
H
Single
Double
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Important Formulas for the Wedge
Mechanical Advantage Load R
Effort E and MA
L H
(Eq. 10)
(Eq. 11)
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Wedge
Ex Given the wedge geometry, and the effort find
the mechanical advantage and the maximum
separation load. Given L 10 , H 4, E
100 lbs. Find MA and R. Equation MA L/H
10/4 2.5 R MA E 2.5 100 250 lbs
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Screw
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Screw- Examples
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Screw The screw is also a modification of the
inclined plane. A screw can be made by wrapping
an inclined plane around a cylinder.
The screw can be used to change from rotary to
straight line (linear) motion.
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Screw- Definitions Screw threads are typically
described as follows 1/4 - 20 UNC
where 1/4 is the outer diameter of the
threads 20 is the number of threads per inch of
screw length UNC refer to Unified National Coarse
thread which is a standard used to define the
details of the thread shape.
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Screw- Definitions
Number of Threads per Inch
OD
1
View A
Pitch
View A
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Screw Screw Pitch is the distance between two
adjacent threads on a screw. Pitch is calculated
from Pitch 1
.
Number of threads per inch
of length Circumference is calculated from
Circumference Pi Diameter
(Eq. 12)
(Eq. 13)
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Important Formulas for the Screw
Mechanical Advantage Load R
Effort
E and Mechanical Advantage Circumference

Pitch or MA C P
(Eq. 14)
(Eq. 15)
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Screw Screws are often turned by another simple
machine such as a wheel and axle or a lever. In
this case the total mechanical advantage is the
circumference of the simple machine that has the
effort applied to it divided by the pitch of the
screw. Ex A screw with 20 threads per inch is
turned by a screwdriver having a handle diameter
of 1. What is the mechanical advantage of the
screw? Pitch 1/20 .05 MA Circumference /
Pitch 3.141 1 / .05 62.82
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Reference Sources Garratt, James, Design and
technology 2nd Edition, Cambridge University
Press, 1996, ISBN 0521556074. The Physics
Classroom, http//www.glenbrook.k12.il.us/gbssci/p
hys/Class/BBoard.html