Simple Machines

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Simple Machines
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Objectives

• To familiarize students with the different
  categories of simple machine.
• Explain how simple machines enhance human
  capabilities.
• Work safely and accurately in a variety of
  experiments.
• Demonstrate curiosity, exhibit motivation for
  learning, and use class time effectively.
• Exhibit and refine inherent personal qualities
  such as creativity and resourcefulness.

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Class Notes

• Simple machines make our work easier by providing
  a mechanical advantage.
• We use less effort/do less work to move an
  object.
• All simple machines belong to one of two families
  
• The inclined plane family and
• The lever family.
• There are six simple machines
• wedge, ramp, screw, lever, wheel and axle, and
  pulley.

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Mechanical Advantage
We know that simple machines make work easier.
Mechanical advantage is a measure of how much
easier or faster our work has become as a result.
Mathematically, this can be calculated as
follows
OR
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Levers

• Levers are one of the basic tools that were
  probably used in prehistoric times.
• Levers were first described about 260 BC by the
  ancient Greek mathematician Archimedes (287-212
  BC).

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.
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Levers
Mechanical Advantage (M.A.)
Length from Fulcrum to Effort
LE Length from Fulcrum to Load (R)
LR
M.A.

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Types of levers

• First class lever
• The fulcrum is located in the center of the lever
  arm and the effort and load are at opposite ends.
  Example Seesaw
• Second class lever
• With a second-class lever the weight is located
  in the middle and the fulcrum and the effort or
  at opposite ends. Example Wheelbarrow
• Third class lever
• The effort is applied at the middle of the arm
  and the weight is held at one end while the
  fulcrum is at the other end. Example Tweezers

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Levers
1st Class 2nd
Class 3rd Class
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Wheel and Axle
A wheel axle can be made from a 2nd or 3rd
class lever.
E
R
Wheel
Wheel
R
E
Axle
Axle
M.A. Radius (L) to Effort (E) LE
Radius (L) to Load (R)
LR
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Wheel and Axle
M.A. Radius (L) to Effort (E) LE
Radius (L) to Load (R) LR
Resistance M.A. Effort
Finds Resistance if the Effort and Mechanical
Advantage are known.
Torque is a twisting force. The units for torque
are typically ft-lbs or inch-lbs. Torque can be
calculated using the formula Torque Force
radius
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Wheel and Axle

• Rotary Motion is the circular motion which occurs
  when the wheel and axle are rotated about the
  centerline axis. Usually rotary motion is defined
  in terms of degrees of revolution.
• Linear Motion is the straight-line motion which
  occurs when a wheel rolls along a flat surface.
  The linear distance traveled when the wheel
  completes one revolution is equal to the
  circumference of the wheel.
• Circumference Pi Wheel diameter

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The Pulley

• A pulley is an adaptation of a wheel and axle.
• A single pulley simply changes the direction of a
  force.
• When two or more pulleys are connected together,
  they permit a heavy load to be lifted with less
  force.
• The trade-off is that the end of the rope must
  move a greater distance than the load.

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The Pulley
M.A. Total number of strands supporting the load
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The Pulley
Equations and Terms
M.A. Total number of strands supporting the load
Finds the Load if the Effort and Mechanical
Advantage are known
Load M.A. Effort
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The Pulley
1. Fixed Pulley is defined when a pulley is
attached or fixed to a strong member, which will
not move. When a fixed pulley is used the force
needed to lift a weight does not change. Notice
that it takes 100 N of force to lift a 100N mass
(no MA). Only the direction of the force applied
is altered. Also note there is no distance
advantage either (i.e. 10cm moves the mass 10cm)
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The Pulley
2.Movable Pulley splits the work in half. The
effort needed to lift 100 N weight is 50 N. The
mechanical advantage of a movable pulley is 2.
Also note that the trade off is that the rope
must be pulled twice as far to lift the object
the same distance as in 1. (i. e. 20cm to move
the mass 10cm)
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The Pulley
3 4. Block and Tackle is a system of three or
more pulleys. It reverses the direction of the
effort so that a downward pull can be used to
lift an object. For number 3, the mechanical
advantage is 3 so that 33 pounds of effort is
needed to lift an object weighing 100N. (The
distance the rope is pulled has tripled.)
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Inclined Plane

• The inclined plane is the simplest machine of all
  the machines.
• An inclined plane is a flat sloping surface along
  which an object can be pushed or pulled.

• An incline plane is used to move an object upward
  to a higher position.

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Inclined Plane
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Inclined Plane
Mechanical Advantage (M.A.)
Mechanical Advantage for the Incline Plane
M.A. Length L Height
H
Force M.A. E
Finds the Force if the Effort (E) and Mechanical
Advantage are known
Effort Force M.A.
This equation is obtained by algebraically
manipulating the equation above.
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The Wedge

1. During its use, an inclined plane remains
   stationary, while the wedge moves.
2. With an inclined plane the effort force is
   applied parallel to the slope of the incline.
3. With a wedge the effort force is applied to the
   vertical edge (height) incline.

M.A. Length L Height
H
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The Wedge
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The Screw
Can be used to change from rotary to straight
line (linear) motion.

• A screw is a combination of two simple machines
• an inclined plane
• a wheel and axle

Inclined Plane
Wheel and Axel
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The Screw
Equations and Definitions
Screw Pitch is the distance between two adjacent
threads on a screw. The formula to calculate
pitch is Pitch
length measured
Number of threads per length measured
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The Screw
Equations and Definitions
The Circumference of the screw is calculated
using the Geometry formula Circumference Pi
Diameter
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The Screw
The formula for the Mechanical Advantage of a
screw is M.A. Circumference Pitch
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Extension
Elements of the engineering-design process can be
used in short term problem-solving activities
a) learn and practice systematic problem solving,
b) develop and apply their creativity and
ingenuity c) make concrete applications of
mathematics and science skills and concepts.
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Mechanical Ball Shooter

• Challenge Problem
• To create a device that will fire a ball
  accurately within a given range.
• Rules
• Must be able to fire a projectile (to be
  specified by the instructor) anywhere within 5
  to 15 operating range (design adjustability into
  your device!)
• Must fit within a 1x1 footprint (in collapsed
  form)
• Cannot utilize high-pressure gases or combustible
  materials
• Must be constructed primarily out of materials
  that are provided and found.