Work

1
Chapter 5

• Work
• and
• Machines

2
Simple machines

• A simple machine is a machine that does work with
  only one movement of the machine.
• There are six types of simple machines
• Inclined planes, wedges, screws, levers, pulleys,
  and the wheel and axle.
• Inclined Plane
• A slanted surface used to raise an object.
• The mechanical advantage of an inclined plane is
  the length of the plane divided by its height.
• Mechanical Advantage Length of Slope Height
  of Slope
• MA l/h
• Because the length of an inclined plane can never
  be shorter than its height, the mechanical
  advantage of an inclined plane can never be less
  than 1.

3
Simple machines

• 2. Wedge
• An inclined plane that moves.
• Usually a piece of wood or metal that is thinner
  at one end.
• The effort force is transferred to the thinner
  end, as a result, a large force is exerted on a
  small surface.
• The longer and thinner the wedge is, the less
  effort is required to overcome a large
  resistance.
• When you sharpen a wedge, you are increasing its
  mechanical advantage by decreasing the effort
  force that must be applied in using it.

4
Simple machines

• 3. Screw
• An inclined plane wrapped around a cylinder to
  form a spiral.
• A screw multiplies the effort force by acting
  through a long effort distance.
• The closer the threads, or ridges, of the screw,
  the greater the mechanical advantage of the screw.

5
Simple machines

• 4. Lever
• A bar that is free to pivot, or move about, a
  fixed point when an effort force is applied.
• The fixed point of the pivot is called the
  fulcrum.
• When an effort force is applied to a lever, the
  lever moves about the fulcrum and overcomes a
  resistance force.
• There are three classes of levers which are all
  based on the positions of the effort force,
  resistance force, and fulcrum.

6
Simple machines

• First class lever
• The fulcrum is between the effort force and the
  resistance force.
• The advantage is that it multiplies the effort
  force and changes its direction.
• Example Scissors
• B. Second class lever
• The resistance force is between the fulcrum and
  the effort force.
• The advantage is that it multiplies the effort
  force but does not change its direction.
• Example Wheelbarrow
• C. Third class lever
• The effort force is between the resistance force
  and the fulcrum.
• Effort force is greater than the resistance
  force.
• The advantage is that it multiplies the distance
  of the effort force .
• Example Bat

7
Simple machines
8
Simple machines

• The mechanical advantage of a lever is the number
  of times the lever increases the effort force.
• It is equal to the resistance force divided by
  the effort force.
• It can also be calculated by using the lengths of
  the effort force and from the fulcrum and the
  resistance force from the fulcrum.
• The distance from the effort force to the fulcrum
  is called the effort arm.
• The distance from the resistance force to the
  fulcrum is called the resistance arm.
• The mechanical advantage of a lever is the length
  of the effort arm divided by the length of the
  resistance arm.
• Mechanical Advantage Effort Arm Length
  Resistance Arm Length
• MA Lin/Lout

9
Simple machines

• 5. Pulley
• A chain, belt, or rope wrapped around a wheel.
• It can change either the direction or the amount
  of an effort force.
• A pulley that is attached to a stationary
  structure is a fixed pulley.
• A fixed pulley cannot multiply an effort force,
  but it can change the direction of an effort
  force and make lifting an object easier.
• The mechanical advantage of a fixed pulley is one.

10
Simple machines

• A pulley that is attached to a rope is called a
  movable pulley.
• It can multiply the effort force, but cannot
  change the direction of the effort force.
• The mechanical advantage of a movable pulley is
  greater than one.
• A greater mechanical advantage can be obtained by
  combining fixed and movable pulleys into a pulley
  system.
• The mechanical advantage of a pulley system is
  approximately equal to the number of the
  supporting ropes.

11
Simple machines
12
Simple machines

• 6. Wheel and Axle
• A lever that rotates in a circle.
• Made of two wheels of different sizes.
• The axle is the smaller wheel.
• The larger wheel turns around the axle.
• The effort force is applied to the wheel and is
  multiplied at the axle.
• The mechanical advantage of a wheel and axle is
  equal to the radius of the wheel divided by the
  radius of the axle.
• Mechanical Advantage Radius of Wheel Radius
  of Axle
• MA rw/ra

13
Simple machines

• A gear is a wheel and axle with the wheel having
  teeth around its rim.
• When the teeth of two gears interlock, turning
  one gear causes the other gear to turn.
• When two gears of different sizes are
  interlocked, they rotate at different rates.
• Each rotation of the larger gear causes the
  smaller gear t make more than one rotation.
• If the input force is applied to the larger gear,
  the output force exerted by the smaller gear is
  less than the input force.
• Gears may also change the direction of the force.

14
Simple machines
15
Simple machines

• A combination of 2 or more simple machines is
  called a compound machine.
• Examples Car, bicycle, watch, can opener,
  typewriter, and your body.
• Compound machines make doing work easier.
• Remember that machines, simple or compound,
  cannot multiply work.
• You can get no more work out of a machine than
  you put into it.

16
Using machines

• A machine is a device that makes doing work
  easier.
• Examples Knives, scissors, doorknobs, forklifts,
  pulleys, etc.
• Machines make work easier by changing the size or
  direction of the applied force.
• Example Screwdriver and pulley.
• Machines also make work easier by increasing the
  distance over which a force can be applied.
• Example Rake.

17
Using machines

• A car jack is a simple example of a machine that
  increases the applied force.
• The upward force exerted by the jack is greater
  than the downward force you exert on the handle.
• However, the distance you push the handle down is
  greater than the distance the car is pushed
  upward.
• Because work is the product of force and
  distance, the work done by the jack is equal to
  the work you do on the jack.
• The jack increases the applied force, but it
  doesnt increase the work done.

18
Using machines

• Some machines change the direction of the force
  that is applied to them.
• An ax blade changes the direction of the force
  from vertical to horizontal, which in turn splits
  the wood apart.

19
Using machines

• Two forces are involved when a machine is used to
  do work, the force you exert on the machine and
  the force that the machine exerts on the object.
• Input Force (Fin) The force that is applied to
  the machine.
• Output Force (Fout) The force applied by the
  machine.
• Example
• When you try to pull a nail out with a hammer,
  you apply the input force to the handle, the
  output force is the force that the claw applies
  to the nail.

20
Using machines

• There are two kinds of work that need to be
  considered when you use a machine the work done
  by you on the machine and the work done by the
  machine.
• Work In (Win) The work done by you on a machine.
• Work Out (Wout) The work done by the machine.
• Remember that energy is always conserved, so the
  amount of energy the machine transfers to the
  object cannot be greater than the amount of
  energy you transfer to the machine.
• A machine cannot create energy, so Wout is never
  greater than Win.

21
Using machines

• However, not all of the energy transferred to a
  machine is transferred into the object.
• When a machine is used, some of the energy
  transferred changes to heat due to friction.
• The energy that changes to heat cannot be used to
  do work, so Wout is always smaller than Win.

22
Using machines

• In an ideal machine (the perfect machine), no
  energy would be lost to friction and all of the
  input work would be converted into output work.
• For an ideal machine
• Win Wout
• Remember, we do not live in a perfect world, so
  we have no perfect machines.

23
Using machines

• Machines like a car jack, a crow bar, and a claw
  hammer make work easier by making the output
  force greater than in input force.
• The ratio of the input force to the output force
  is the mechanical advantage of a machine.
• Mechanical Advantage Output Force Input Force
• MA Fout/Fin
• There are NO units for mechanical advantage since
  you are dividing the output force in newtons by
  the input force in newtons.
• The mechanical advantage of a machine without
  friction is called ideal mechanical advantage
  (IMA).

24
Using machines

• Example
• Calculate the mechanical advantage of a hammer if
  the input force is 125-N and the output force is
  2000-N.
• MA Fout/Fin
• MA 2000-N/125-N
• MA 16
• This means that the hammer has increased your
  force by a factor of 16.

25
Using machines

• Example
• What is the mechanical advantage of a crowbar
  when you apply 100-N of force to lift a 250-N
  rock.
• MA Fout/Fin
• MA 250-N/100-N
• MA 2.5

26
Using machines

• Efficiency is a measure of how much of the work
  put into a machine is changed into useful output
  work by the machine.
• A machine with high efficiency produces less heat
  from friction so more of the input work is
  changed into useful output work.
• Efficiency (Output Work Input Work) 100
• E (Wout/Win) 100
• Efficieny is expressed as a percent.

27
Using machines

• Example
• Find the efficiency of a machine that does 800-J
  of work if the input work is 2400-J.
• E (Wout/Win) 100
• E (800/2400) 100
• E 33.3
• This means that the machine only converts 33.3
  of the energy put into the machine into energy
  put out by the machine. The other 66.7 of the
  energy is lost due to friction.

28
Using machines

• In an ideal machine, the efficiency is 100.
• In a real machine, friction causes the output
  work to always be less than the input work, so
  the efficiency of a real machine is always less
  than 100.
• Machines can be made more efficient by reducing
  friction, by adding a lubricant.
• A lubricant fills in the gaps between the
  surfaces, enabling the surfaces to slide past
  each other more easily.

29
Work

• What is work?
• Work is the transfer of energy that occurs when a
  force makes an object move.
• Work Force Distance
• W Fd
• Units for work Newtonmeter (Nm) or Joule (J)
• In order to be working, two conditions must be
  met
• A force must be applied.
• The force must make an object move in the same
  direction as the force.
• If the object does not move, then no work is
  being done.

30
Work

• Example
• You push a refrigerator with a force of 100-N. If
  you move the refrigerator a distance of 5-m, how
  much work do you do?
• Work Force Distance
• Work (100-N) (5-m)
• Work 500-J

31
Work

• Example
• A force of 75-N is exerted on a 45-kg couch and
  the couch is moved 5-m. How much work is done in
  moving the couch?
• Work Force Distance
• Work (75-N) (5-m)
• Work 375-J

32
Work

• Example
• A lawn mower is pushed with a force of 80-N. If
  12 000-J of work are done in mowing a lawn, what
  is the total distance the lawn mower was pushed?
• Work Force Distance
• 12000-J 80-N Distance
• Distance (12000-J) (80-N)
• Distance 150-m

33
Work

• Example
• The brakes on a car do 240 000-J of work in
  stopping the car. If the car travels a distance
  of 50-m while the brakes are being applied, what
  is the total force the brakes exert on the car?
• Work Force Distance
• 240000-J Force 50-m
• Force (240000-J) (50-m)
• Force 4800-N

34
Work

• Power is the rate at which work is done, or the
  amount of work done per unit time.
• Power Work Time
• P W/t
• P Fd/t
• Units for power Nm/sec or J/sec or Watt (W) or
  kilowatts (kW) for large quantities.
• In the U.S., we measure power in another unit,
  horsepower.
• Horsepower gets its name from horses since they
  were the most common source of power in the 18th
  century.
• 1 horsepower (hp) 745.56 watts

35
Work

• Example
• You do 900-J of work pushing a sofa. If it took
  5-seconds to move the sofa, what was your power?
• Power Work Time
• Power (900-J) (5-sec)
• Power 180-W

36
Work

• Example
• To lift a baby from a crib 50-J of work are done.
  How much power is needed if the baby is lifted in
  0.5-seconds?
• Power Work Time
• Power (50-J) (0.5-sec)
• Power 100-W

37
Work

• Example
• If a runners power is 130-W, how much work is
  done by the runner in 10-minutes?
• Power Work Time
• 130-W Work 600-sec
• Work (130-W) (600-sec)
• Work 78000-J

38
Work

• Example
• The power produced by an electric motor is 500-W.
  How long will it take the motor to do 10 000-J of
  work?
• Power Work Time
• 500-W 10000-J Time
• 500-W Time 10000-J
• Time (10000-J) (500-W)
• Time 20-sec

39
Work

• Recall that energy is the ability to cause a
  change, you can also think that energy is the
  ability to do work.
• When you do work on an object, you increase its
  energy.
• Energy is always transferred from the object that
  is doing the work to the object on which the work
  is done.
• Power is also the rate at which energy is
  transferred.
• Power Energy Transferred Time
• P E/t
• Example
• A light bulb Energy is transferred from the
  circuit to the lightbulb filament. The filament
  converts the electrical energy into heat and
  light. The power used by the lightbulb is the
  amount of electrical energy transferred to the
  lightbulb each second.