Principles of Technology/Physics in Context (PT/PIC)

1
Principles of Technology/Physics in Context
(PT/PIC)

• Chapter 7
• Work and Energy 4
• Text p. 135 - 136

2
Principles of Technology/Physics in Context
(PT/PIC)

• During the lecture assessment questions will be
  asked.
• The assessment questions will be collected at the
  end of the lecture for grading.

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Key Objectives

• At the conclusion of this chapter youll be able
  to
• Solve problems involving simple machines.
• List other types of simple machines.

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7.4 SIMPLE MACHINES AND WORK

• A simple machine is a mechanical device that
  changes the direction or magnitude of a force.

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7.4 SIMPLE MACHINES AND WORK

• In general, they can be defined as the simplest
  mechanisms that use mechanical advantage (also
  called leverage) to multiply force.

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7.4 SIMPLE MACHINES AND WORK

• A simple machine uses a single applied force to
  do work against a single load force.
• Ignoring friction losses, the work done on the
  load is equal to the work done by the applied
  force.

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7.4 SIMPLE MACHINES AND WORK

• They can be used to increase the amount of the
  output force, at the cost of a proportional
  decrease in the distance moved by the force.
• The ratio of the output to the input force is
  called the (Actual) mechanical advantage.
• MA load / applied force Fout/Fin

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7.4 SIMPLE MACHINES AND WORK

• Usually the term refers to the six classical
  simple machines which were defined by Renaissance
  scientists
• Inclined plane
• Pulley
• Lever
• Wedge
• Screw
• Wheel and axle

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7.4 SIMPLE MACHINES AND WORK

• They are the elementary "building blocks" of
  which all complicated machines are composed.
• For example, wheels, levers, and pulleys are all
  used in the mechanism of a bicycle.

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7.4 SIMPLE MACHINES AND WORK Incline Plane

• The inclined plane is one of the original six
  simple machines as the name suggests, it is a
  flat surface whose endpoints are at different
  heights.

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7.4 SIMPLE MACHINES AND WORK Incline Plane

• By moving an object up an inclined plane rather
  than completely vertical, the amount of force
  required is reduced, at the expense of increasing
  the distance the object must travel.

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7.4 SIMPLE MACHINES AND WORK Inclined Plane

• The (Ideal) Mechanical Advantage (MA)of the
  inclined plane if we ignore friction
• MA length of the plane / the height of the
  plane din/dout

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Assessment Question 1

• Calculate the Mechanical Advantage (MA) of an
  incline plane that has a length of 27 m (din) and
  a height of 3 m (dout).
• MA length / height din/dout
• MA 27 m / 3 m
• 3 C. 30
• 9 D. 81

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7.4 SIMPLE MACHINES AND WORK Inclined Plane

• Examples include
• Ramps, chutes and slides
• Blades, foils, (wings)
• Wedges, saws and chisels

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• A pulley, also called a sheave or a drum, is a
  mechanism composed of a wheel on an axle or shaft
  that may have a groove between two flanges around
  its circumference.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• A rope, cable, belt, or chain usually runs over
  the wheel and inside the groove, if present.
• Pulleys are used to change the direction of an
  applied force, transmit rotational motion, or
  realize a mechanical advantage in either a linear
  or rotational system of motion.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• A belt and pulley system is characterized by two
  or more pulleys in common to a belt.
• This allows for mechanical power, torque, and
  speed to be transmitted across axes and, if the
  pulleys are of differing diameters, a mechanical
  advantage to be realized.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• Two or more pulleys together are called a block
  and tackle.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• Also called block and tackles, rope and pulley
  systems (the rope may be a light line or a strong
  cable) are characterized by the use of one rope
  transmitting a linear motive force (in tension)
  to a load through one or more pulleys for the
  purpose of pulling the load (often against
  gravity.)

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• In a system of a single rope and pulleys, when
  friction is neglected, the mechanical advantage
  gained can be calculated by counting the number
  of rope lengths exerting force on the load.
• Mechanical Advantage Number of ropes pulling on
  Load

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Assessment Question 2

• All of the following are true EXCEPT
• A pulley is composed of a wheel on an axle with a
  rope running over the wheel.
• Pulleys are used to change the direction of an
  applied force, transmit rotational motion, or
  realize a mechanical advantage .
• Two or more pulleys together are called a juke
  and high step.
• In a single rope and pulleys system the
  mechanical advantage is the number of rope
  lengths on the load.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• Since the tension in each rope length is equal to
  the force exerted on the free end of the rope,
  the mechanical advantage is simply equal to the
  number of ropes pulling on the load.
• Mechanical Advantage Number of ropes pulling on
  Load

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• In the above figure, if you are going to suspend
  the weight in the air then you have to apply an
  upward force of 100 pounds to the rope.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• If the rope is 100 feet (30.5 meters) long and
  you want to lift the weight up 100 feet, you have
  to pull in 100 feet of rope to do it.
• This is simple and obvious.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• The only thing that changes is the direction of
  the force you have to apply to lift the weight.
• You still have to apply 100 pounds of force to
  keep the weight suspended, and you still have to
  reel in 100 feet of rope in order to lift the
  weight 100 feet.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• You can see that the weight is now suspended by
  two pulleys rather than one.
• That means the weight is split equally between
  the two pulleys, so each one holds only half the
  weight, or 50 pounds (22.7 kilograms).

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• If you want to lift the weight 100 feet higher,
  then you have to reel in twice as much rope 0-
  200 feet of rope must be pulled in.

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• This demonstrates a force-distance tradeoff. The
  force has been cut in half but the distance the
  rope must be pulled has doubled

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7.4 SIMPLE MACHINES AND WORK PULLEYS

• The following diagram adds a third and fourth
  pulley

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Assessment Question 3

• Determine the number of ropes exerting force on a
  2000 N load (Fout) that is lifted with 400 N
  (Fout) of force. 150 m (din) of rope is need to
  lift the load 30 m (dout).
• MA Number of ropes pulling on Load
• MA Fout/Fin 2000 N / 400 N
• MA din/dout 150 m / 30 m
• 2 C. 5
• 4 D. 10

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7.4 SIMPLE MACHINES AND WORK LEVERS

• In physics, a lever (from French lever, "to
  raise", c.f. a levant) is a rigid object that is
  used with an appropriate fulcrum or pivot point
  to multiply the mechanical force that can be
  applied to another object.
• This leverage is also termed mechanical
  advantage, and is one example of the principle of
  moments.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• Archimedes once said, "Give me a lever long
  enough and a fulcrum on which to place it, and I
  shall move the world."
• First class levers are similar but not the same
  as second or third class levers, in which the
  fulcrum, resistance, and effort are in different
  locations.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• The principle of leverage can be derived using
  Newton's laws of motion, and modern statics.
• It is important to note that the amount of work
  done is given by force times distance.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• To use a lever to lift a certain unit of weight
  with a force of half a unit, the distance from
  the fulcrum to the spot where force is applied
  must be exactly twice that of the distance
  between the weight and the fulcrum.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• For example, to cut in half the force required to
  lift a weight resting 1 meter from the fulcrum,
  we would need to apply force 2 meters from the
  other side of the fulcrum.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• The amount of work done is always the same and
  independent of the dimensions of the lever (in an
  ideal lever). The lever only allows to trade
  force for distance.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• The point where you apply the force is called the
  effort.
• The effect of applying this force is called the
  load.
• The load arm and the effort arm are the names
  given to the distances from the fulcrum to the
  load and effort, respectively.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• Using these definitions, the Law of the Lever is
• Load arm x load force effort arm x effort
  force.

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7.4 SIMPLE MACHINES AND WORK LEVERS

• If, for example, a 1 gram feather were balanced
  by a one kilogram rock, the feather would be 1000
  times further from the fulcrum than the rock

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7.4 SIMPLE MACHINES AND WORK LEVERS

• if a 1 kilogram rock were balanced by another 1
  kilogram rock, the fulcrum would be in the middle.

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Assessment Question 4

• Determine the length of the effort arm to balance
  on a 495 kg load (Load Force) with a 55 kg (Fout)
  student if the load is 2 m (load arm) from the
  fulcrum.
• Load arm x load force effort arm x effort
  force.
• Effort arm (load arm x load force) / effort
  force
• Effort arm (2 m x 495 kg) / 55 kg
• 18 m C. 545 m
• 99 m D. 2495 m

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7.4 SIMPLE MACHINES AND WORK LEVERS

• There are three classes of levers which represent
  variations in the location of the fulcrum and the
  input and output forces.

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7.4 SIMPLE MACHINES AND WORK 1st Class LEVERS

• A first-class lever is a lever in which the
  fulcrum is located between the input effort and
  the output load.

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7.4 SIMPLE MACHINES AND WORK 1st Class LEVERS

• In operation, a force is applied (by pulling or
  pushing) to a section of the bar, which causes
  the lever to swing about the fulcrum, overcoming
  the resistance force on the opposite side.

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7.4 SIMPLE MACHINES AND WORK 1st Class LEVERS

• The fulcrum may be at the center point of the
  lever as in a seesaw or at any point between the
  input and output.

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7.4 SIMPLE MACHINES AND WORK 1st Class LEVERS

• Examples
• Seesaw (also known as a teeter-totter)
• Trebuchet
• Crowbar (curved end of it)
• Hammer Claw, when pulling a nail with the
  hammer's claw
• Hand trucks are L-shaped but work on the same
  principle, with the axis as a fulcrum
• Pliers (double lever)
• Scissors (double lever)
• Shoehorn (used for putting feet into shoes)
• Wheel and axle because the wheel's motions
  follows the fulcrum, load arm, and effort arm
  principle.
• Chopsticks with hand the middle finger acts as a
  pivot. The whole system is a double lever

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7.4 SIMPLE MACHINES AND WORK 2nd Class LEVERS

• In a second class lever the input effort is
  located at the end of the bar and the fulcrum is
  located at the other end of the bar, opposite to
  the input, with the output load at a point
  between these two forces

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7.4 SIMPLE MACHINES AND WORK 2nd Class LEVERS

• Examples
• Bottle opener
• Crowbar (flat end)
• Curb bit
• Dental elevator
• Wheelbarrow
• Wrench
• Nutcracker
• Doorknob (could be a wheel and axle also)
• Nail clippers, the main body handle exerts the
  incoming force
• Oar the water is the fulcrum the boat is the
  load and the effort is at the inboard end

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7.4 SIMPLE MACHINES AND WORK 3rd Class LEVERS

• For this class of levers, the input effort is
  higher than the output load, which is different
  from second-class levers and some first-class
  levers.

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7.4 SIMPLE MACHINES AND WORK 3rd Class LEVERS

• However, the distance moved by the resistance
  (load) is greater than the distance moved by the
  effort.

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7.4 SIMPLE MACHINES AND WORK 3rd Class LEVERS

• Since this motion occurs in the same length of
  time, the resistance necessarily moves faster
  than the effort.

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7.4 SIMPLE MACHINES AND WORK 3rd Class LEVERS

• Thus, a third-class lever still has its uses in
  making certain tasks easier to do.

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7.4 SIMPLE MACHINES AND WORK 3rd Class LEVERS

• In third class levers, effort is applied between
  the output load on one end and the fulcrum on the
  opposite end.

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7.4 SIMPLE MACHINES AND WORK 3rd Class LEVERS

• Examples
• Baseball bat
• Boat paddle
• Broom, Hammer
• Electric gates
• Fishing rod
• Hockey stick
• Human arm
• Tennis racket
• Tongs, Tweezers
• Stapler
• Mousetrap (Spring-loaded bar type)
• Shovel (the action of picking or lifting up sand
  or dirt)

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Assessment Question 5

• All of the following are true EXCEPT
• A first-class lever is a lever in which the
  fulcrum is located between the input effort and
  the output load.
• In a second class lever the input effort is
  located at the end of the bar and the fulcrum is
  located at the other end of the bar, opposite to
  the input, with the output load at a point
  between these two forces
• In third class levers, effort is applied between
  the output load on one end and the fulcrum on the
  opposite end.
• For all classes of levers, the input effort is
  higher than the output load.

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7.4 SIMPLE MACHINES AND WORK WEDGE

• A wedge is a triangular shaped tool, a compound
  and portable inclined plane, and one of the six
  classical simple machines.

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7.4 SIMPLE MACHINES AND WORK WEDGE

• It can be used to separate two objects or
  portions of an object, lift an object, or hold an
  object in place.

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7.4 SIMPLE MACHINES AND WORK WEDGE

• It functions by converting a force applied to its
  blunt end into forces perpendicular (normal) to
  its inclined surfaces.

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7.4 SIMPLE MACHINES AND WORK WEDGE

• The mechanical advantage of a wedge is given by
  the ratio of the length of its slope to its
  width.

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7.4 SIMPLE MACHINES AND WORK WEDGE

• Although a short wedge with a wide angle may do a
  job faster, it requires more force than a long
  wedge with a narrow angle.

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7.4 SIMPLE MACHINES AND WORK WEDGE

• The mechanical advantage of a wedge can be
  calculated by dividing the length of the slope by
  the wedge's width
• Mechanical Advantage length / thickness

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Assessment Question 6

• Calculate the Mechanical Advantage (MA) of a
  wedge that has a length of 72 m (din) and a
  thickness of 3 m (dout).
• MA length / thickness din/dout
• MA 72 m / 3 m
• 9 C. 24
• 15 D. 48

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7.4 SIMPLE MACHINES AND WORK SCREW

• A screw is a shaft with a helical groove or
  thread formed on its surface and provision at one
  end to turn the screw.
• Its main uses are as a threaded fastener used to
  hold objects together, and as a simple machine
  used to translate torque into linear force.

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7.4 SIMPLE MACHINES AND WORK SCREW

• It can also be defined as an inclined plane
  wrapped around a shaft.
• Screws come in a variety of shapes and sizes for
  different purposes.

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7.4 SIMPLE MACHINES AND WORK SCREW

• The ratio of threading determines the mechanical
  advantage of the machine.
• More threading increases the mechanical
  advantage.

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7.4 SIMPLE MACHINES AND WORK SCREW

• The vertical distance between two adjacent screw
  threads is called the pitch of a screw.
• One complete revolution of the screw will move it
  into an object a distance to the pitch of the
  screw.

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7.4 SIMPLE MACHINES AND WORK SCREW

• The pitch of any screw can be calculated as
  follows
• Pitch Number of threads/inch of screw

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7.4 SIMPLE MACHINES AND WORK SCREW

• As an example, assume that you place a ruler
  parallel to a screw and count 10 threads in a
  distance of one inch.
• The pitch of the screw would be 1/10.

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Assessment Question 7

• All of the following are true EXCEPT
• A screw can be defined as an inclined plane
  wrapped around a shaft.
• More threading on a screw increases the
  mechanical advantage.
• One complete revolution of the screw will move it
  into an object a distance to the pitch of the
  screw.
• If a screw has 20 threads per inch the pitch of
  the screw will be 20.

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7.4 SIMPLE MACHINES AND WORK SCREW

• The Mechanical Advantage (M.A.) is equal to the
  circumference of the screw divided by the pitch
  of the screw.
• M.A. circumference/pitch

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7.4 SIMPLE MACHINES AND WORK SCREW

• The Mechanical Advantage (M.A.) is equal to the
  circumference of the screw multiplied by the
  number of threads per unit (inch, cm) of the
  screw.
• M.A. circumference x (number of threads/ unit
  (inch, cm)

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Assessment Question 8

• Calculate the Mechanical Advantage (MA) of a
  screw that as a radius of 0.05 m (r) is and has
  500 threads per meter.
• MA circumference(number of threads/m)
• MA 2pr(number of threads/m)
• MA 2(3.140.05 m)(500 threads/m)
• 12 C. 160
• 85 D. 550

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7.4 SIMPLE MACHINES AND WORK Wheel and Axle

• The wheel and axle is a simple machine consisting
  of a large wheel rigidly secured to a smaller
  wheel or shaft, called an axle.
• When either the wheel or axle turns, the other
  part also turns.

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7.4 SIMPLE MACHINES AND WORK Wheel and Axle

• One full revolution of either part causes one
  full revolution of the other part.
• If the wheel turns and the axle remains
  stationary, it is not a wheel and axle machine.

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7.4 SIMPLE MACHINES AND WORK Wheel and Axle

• When the force is applied to the wheel in order
  to turn the axle, force is increased and distance
  and speed are decreased.

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Assessment Question 9

• All of the following are true EXCEPT
• The wheel and axle is a simple machine consisting
  of a large wheel rigidly secured to a smaller
  wheel or shaft, called an axle.
• When either the wheel or axle turns, the other
  part also turns. One full revolution of either
  part causes one full revolution of the other
  part.
• In wheel and axle machines the wheel turns and
  the axle remains stationary.
• When the force is applied to the wheel in order
  to turn the axle, force is increased and distance
  and speed are decreased.

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7.4 SIMPLE MACHINES AND WORK Wheel and Axle

• The mechanical advantage of a wheel and axle is
  the ratio of the radius of the wheel to the
  radius of the axle. M.A. rwheel/raxle

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7.4 SIMPLE MACHINES AND WORK Wheel and Axle

• In the wheel and axle illustrated below, the
  radius of the wheel is five times larger than the
  radius of the axle. M.A. rwheel/raxle 5/1

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7.4 SIMPLE MACHINES AND WORK Wheel and Axle

• Therefore, the mechanical advantage is 51 or 5.
• M.A. rwheel/raxle 5/1 5

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Conclusion

• Simple machines provide examples of how work can
  be used to a persons advantage in performing
  such chores as lifting heavy objects and exerting
  large forces that can accomplish a task such as
  cutting through steel.

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Assessment Question 10

• Calculate the Mechanical Advantage (MA) of a
  wheel and axle that as an axle radius of 5 inches
  (raxle) and a wheel radius of 55 inches (rwheel).
• M.A. rwheel/raxle 55/5
• 11
• 25
• 60
• 275