Chapter 10 Glencoe Physics

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Chapter 10 Glencoe Physics

• Energy, Work, and Simple Machines
• 2006

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A. What is work?

• 1. Websters Definitions
• a. energy expended by a natural phenomenum
• b. activity in which one exerts strength to do
  something

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2. Physics Definition of Work

• a. Product of a force acting on an object and the
  displacement of the object in the direction of
  the force
• b. W F s
• (1) work is a scalar quantity
• (2) displacement is critical - w/o movement no
  work is done

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c. SI unit of work is the Newton-meter or JOULE

• (1) A joule is the work done by a force of one
  newton as it acts through a distance of one meter
  along the line of the force
• (2) Also use the joule to measure energy
• d. Other units of work include the foot-pound,
  the erg, and the electron-volt (eV)

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3. Examples of work calculations

• a. A person exerts a vertical force of 30.0N on
  a pail as the pail is carried a horizontal
  distance of 8.0 m at a constant speed. How much
  work does the 30N force do on the pail?
• You do no work, as the force is not along the
  lines of the distance moved. It would have to
  have been moved vertically for work to be done.

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b. How much work do you do on an object of weight
mg as

• (1) you lift it a distance of h meters straight
  up at constant speed and, (2) you lower it
  through this same distance at a constant speed?
• To lift you pull up on the object with a force F
  mg to counteract the weight
• W F s m g h
• When you lower the object F and s are in
  opposite directions, so W m g (-h) -mgh

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4. Work and the Direction of Force

• a. Only the component of the force in the
  direction of movement does work. The component
  of force perpendicular to the direction of motion
  does NO work.
• Key Point to Remember - What is critical is to
  determine the component of force in direction of
  motion

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b. Note as seen in a previous example you can
have negative work

• (1) although work is a scalar quantity, negative
  work means the force is applied in the opposite
  direction from the objects motion.
• (2) Work is also cumulative, so negative work
  will offset positive work.

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• c. Example. Motion is in the x -direction

Fy
F
?
Fx
Motion
s
w Fx s (F cos ?) s F s cos? ? is the angle
between the applied forces direction and the
direction of motion
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d. Special Work cases

• (1) ? 0o, cos? 1 and W F s
• (2) ? 180o, cos? -1 and W -F s
• (3) ? 90o, cos? 0 and W 0
• (4) Note that if you push an object from point A
  to point B and then back to A, you would have no
  displacement, so net work done is zero.

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e. Example A man cleaning his apartment pulls a
vacuum cleaner with a force of 50N and angle of
30o to the horizontal. A frictional force of 40
N retards his motion, and the vacuum is pulled a
distance of 3 meters.

• (1) Calculate the work done by the 50N force
• (2) Calculate the work done by the frictional
  force
• (3) Calculate the net work done on the vacuum by
  all forces acting on it.

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• First draw a picture or free body diagram

FN
FA 50N
Ff40N
motion
W m g
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• W app force (F cos?)s (50N cos30o)(3 m)
  130 Joules
• Wf (Ff cos?) s (40 cos 180o)(3m) -120
  Joules (work is being done on the vacuum by
  rug)
• m g and FN do no work, so Wnet Wf WAF

FN
FA 50N
Ff40N
?30
motion
W m g
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5. Kinetic Energy

• a. energy itself is the ability of an object to
  produce a change in itself or in the world around
  it
• b. KE is the energy an object has due to its
  motion
• c. KE ½ mv2
• Mass, m, is in kilograms
• Velocity , v, is in m/s
• KE is measured in Joules

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6. The Work-Energy Theorem

• a. work is equal to the change in energy that an
  object undergoes
• b. work is the transfer of energy by mechanical
  means.
• c. first established by Joule in nineteenth
  century
• d. energy transfer can go both ways from work
  on an object that increase the objects energy or
  work done by the object so that it transfers
  energy to its surroundings.

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7. Force versus displacement Curve

• a. A graph which shows how force is applied to an
  object with respect to the objects displacment
  from the starting point.
• b. Area under the curve is the work done by the
  force over that distance. Note that a negative
  force means it is being applied in the opposite
  direction from motion.
• c. Area is cumulative. Negative offsets positive

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B. Power

• 1. Power is the work done in a unit of
  time Power Work Done time to do
  work P W / t
• 2. Basic units - work is in joules, time is in
  seconds, and power is in watts
• a. 1 kilowatt 1000 watts
• b. 1 horsepower 746 watts

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Please note that power is the timed rate at which
work is being done.

• 3. Examples
• a. A motor lifts a 200 kg object straight up at a
  constant speed of 3.00 cm/sec. What power is
  being developed by the motor? Express your
  answer in watts and horsepower.

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• Givens
• Constant velocity so Fmotor m g
• m 200 kg
• v 3.00 cm/sec 0.0300 m/s so in one second the
  object moves 0.0300 m
• s 0.0300 m
• t 1 sec
• w m g 1960 N
• Find P. P w / t and W F s

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• W 58.8 J
• P W / t 58.8 J / 1 sec 58.8 watts
  58.8 watts ( 1 HP/ 746 watts) 0.0788 HP
• NOTE Pavg W / time F (?s)/ ?t F
  vavg so power can be determined if you
  know a force causes an object to move a given
  distance at a constant speed

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b. What average power is developed by an 800N
physics teacher while running at a constant speed
up a flight of stairs rising 6 meters if he takes
8 seconds to complete the climb?

• Givens
• F w 800 N
• v constant
• s 6 meters
• t 8 sec
• P F s / t
• P 600 watts

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c. A 50 kg student climbs a rope 5 m in length at
a uniform speed and stops at the top. (1) What
must her average speed have been in order to
match the power output of a 200 watt bulb (2)
how much work did she do and (3) how long did it
take her to climb the rope?

• Givens
• m 50 kg
• s 5 m
• constant velocity so F m g
• P 200 watts
• P F v so v P / F

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• v P / F 0.41 m/s
• W F s 490 N (5 m) 2450 Joules
• t W / P 2450 Joules / 200 watts 12.5 sec

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C. Machines 1. What is a machine?

• a. A device by which the magnitude, direction, or
  method of application of a force is changed so as
  to achieve some advantage.
• b. NOTE A machine does not change the amount of
  work done and does not make the amount of work
  done less, just makes it easier for someone to do
  a job.

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c. Simple machines

• lever - three classes determined by the
  relationship between the applied force, load, and
  fulcrum point
• pulley
• inclined plane (wedge)
• wheel and axle
• screw

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d. complex machines are made up of simple
machines2. Mechanical Advantage (MA)

• a. Use a machine NOT to lessen work but usually
  to lessen the force required to do the work, to
  make the output work easier to achieve
• b. Concerned with the work into a machine and the
  work out of the machine

Ideal Machine
Win
Wout
Win Wout
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c. In a real machine, however, this does not
occur and Wout lt Win

• (1) Reason - input work energy is converted to
  heat due to friction
• (2)

Wout
Win
Real Machine
Thermal Energy
Win gt Wout
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d. Mechanical Advantage MA Fout / Fin

• (1) Force ratio, so unit-less quantity
• (2) If MA gt 1, then machine has increased the
  force you applied to the object moved
• (3) NOTE the machine did not lessen the work
  output or input in any way.

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e. Ideal Mechanical Advantage (IMA)

• (1) IMA Din / D out
• (2) This is the Distance Ratio, and again it is
  unitless
• (3) Design a machine to have a given IMA, then
  work to maximize efficiency and MA

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3. Efficiency

• (1) A ratio between MA and IMA expressed as a
  percent
• (2) Efficiency MA / IMA x 100
  W out / W in x 100

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4. Examples

• a. A bottle opener required a force of 35N to
  lift the cap of a bottle 0.90cm. The opener has
  an IMA of 8.0 and an efficiency of 75.
• (1) What type of simple machine is the basis for
  the opener?
• (2) What is the MA of the opener?
• (3) What force is applied to the bottle cap?
• (4) How far does the handle of the opener move?

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• hardest part in any problem is to identify what
  items are what
• what force is applied to the bottle cap? is
  asking for the Force out of the machine
• And, How far does the handle of the opener
  move? is asking for the Distance in
• If you get confused, remember a machine is used
  to lessen the force in, and it does this by
  trading distance for force. So the distance in
  will always be greater than distance out and
  Force out gt force in.

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• Givens
• Fin 35N
• D out 0.90 cm 0.0090m
• IMA 8.0
• Efficiency 75
• eff MA / IMA x 100
• MA eff x IMA .75 (8.0) 6.0 note
  efficiency was converted to a decimal
• MA F out / F in

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so F out MA (F in) (6.0)(35N) 210N

• IMA D in / D out so D in IMA
  (D out) 8.0 (0.90cm) 7.2 cm

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b. A worker uses a pulley to raise a 225 N carton
10 meters. A force of 110 N is required and the
rope is pulled 30 m.

• (1) What is the MA of the system? (2) What
  is the IMA of the system? (3) What is the
  efficiency of the system?
• Givens
• F out 225N F in 110N
• D out 10 m D in 30 m
• MA 2.05 IMA 3.0 eff 68

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QUIZ - on separate sheet of paper

• What is the efficiency of a pulley if a force of
  650 N acting through 15 meters is required to
  lift a 11,000 N crate up a distance of 0.750
  meters?