Work

1
Chapter 5

• Work
• and
• Energy

2
WORK

• Work is the energy transferred into or out of a
  system through the action of a force.
• Work is the change in energy of a system from the
  application of a force acting over a distance.
• Work is the product of the magnitudes of the
  component of a force along the direction of
  displacement and the displacement.
• Work Force ? Distance
• Units Newton?meters (N?m) or Joules (J)
• 1 N?m 1 J
• 1 J 0.7376 ft?lb (U.S. Customary Units)
• 1 ft?lb 1.356 J

3
WORK

• At the heart of the concept of work is the notion
  of movement against resistance (gravity,
  friction, inertia, etc.)
• Consider the following
• A student holds a heavy weight at arms length for
  several minutes.
• A student carries a heavy weight along a
  horizontal path while walking at a constant
  velocity.
• Which student did work?

4
WORK

• As long as the object moves along the
  line-of-action of the force while the force acts
  on it, work is being done.
• Example
• A man sitting on a sheet of plastic is pulled a
  distance of 2.0 m along a smooth floor by a woman
  exerting a force of 20 N, how much work is done?

5
WORK

• Positive work is done on an object when the point
  of application of the force moves in the
  direction of the force.
• Negative work is done on an object when the point
  of application of the force moves in the opposite
  direction of the force.
• Example
• Raise a 100-kg barbell into the air against the
  downward weight and you do positive work.
• Lower the barbell to the floor and you have done
  negative work.

6
WORK

• The sign of work is important because it will
  tell you whether the object is speeding up or
  slowing down.
• If the net work is positive, the object is
  speeding up and the net force does work on the
  object.
• If the net force is negative, the object slows
  down and work is done by the object on another
  object.

7
WORK

• Example
• A locomotive exerts a constant forwardly directed
  force of 400 kN on a train that it pulls for 500
  m along a straight run. How much work does the
  engine do on the train?

8
WORK

• Example
• Coming toward a station, the locomotive in the
  previous example slows the train, applying a
  constant force of 100 kN in the opposite
  direction. How much work does it then do on the
  train over a distance of 1000 m?

9
WORK

• Imagine an object being pulled along by a person
  tugging on a rope that makes an angle (?) with
  the direction of motion.
• Part of the force acts upward tending to lift the
  object and lessen the load, and part acts in the
  direction of the motion and does work.
• The force is a vector it has two perpendicular
  components, one vertical (F sin ?) and the other
  horizontal (F cos ?).

10
WORK

• Work can only be done by a force if it is applied
  to an object that subsequently begins to move or
  is already moving.
• The work done on a body by a constant applied
  force is the product of the component of the
  force in the direction of the motion multiplied
  by the distance over which it acts.
• Work (F cos ?)d

11
WORK

• Example
• A man sitting on a sheet of plastic is pulled a
  distance of 2.0 m along a smooth floor by a woman
  exerting a force of 20 N at an angle of 30?, how
  much work is done?

12
WORK

• Example
• A truck is dragging a stalled car up a 20?
  incline. The tensile force on the towline is
  constant, and the two vehicles accelerate at a
  constant rate. If the cable makes an angle of 30?
  with the road and the tension is 1600 N, how much
  work was done by the truck on the car in pulling
  it 0.50 km up the incline?

13
WORK

• Example
• How much work is done on a vacuum cleaner pulled
  3.0 m by a force of 50.0 N at an angle of 30.0?
  above the horizontal?

14
WORK

• In general, work is done to overcome some force,
  and one of the most common situations involves
  simply raising a mass against gravity.
• The work done against gravity can be calculated
  by the following equation
• Work Weight ? height mgh

15
WORK

• Example
• A rigid 1.0 kg block is raised at a constant
  speed through a vertical distance of 2.0 m at the
  Earths surface. Determine the work done on the
  block by the hand in overcoming gravity.

16
WORK

• Think about an object being pushed at a constant
  speed in a straight line along the floor by an
  applied force.
• Because the object is not accelerating, the sum
  of the forces must be zero and F must be equal in
  magnitude and opposite in direction to the force
  of kinetic friction (Fk).
• Since the force of kinetic friction is constant,
  the work done in overcoming kinetic friction is
• Work Fkd ?kFnd

17
WORK

• Example
• A youngster weighing 250 N is sitting on the
  grass holding on to a large dog via a leash
  stretched horizontally. The dog pulls on the
  leash with a force of 100 N and drags the kid at
  a constant speed 20 m straight across the yard
  and then stops. How much work did the dog do on
  the child and the ground in overcoming kinetic
  friction?

18
WORK

• Example
• A locked car weighing 6.0 kN has its parking
  brake on. The coefficient of kinetic friction for
  rubber on concrete is 1.
• What will be the value of the friction force on
  the car once it is set in motion?
• What force must be exerted horizontally to slide
  the car at a slow constant speed?
• How much work will be expended in pushing the
  car, very slowly, 10.0 m horizontally?

19
ENERGY

• What is energy?
• The nontechnical usage derives from the Greek en
  (which means in) and ergon (which means work).
• Energy is the capacity to do work.
• In very general terms, energy describes the state
  of a system in relation to the action of the four
  forces.
• It is a property of all matter and is observed
  indirectly through changes in speed, mass,
  position, and so forth.

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ENERGY

• Force is the agent of change energy is a measure
  of change.
• Energy is the measure of the change that has
  occurred, and the change that is yet to occur.
• Energy is a scalar quantity associated in various
  amounts with all the things that exist.
• Energy is not an entity in and of itself there
  is no such thing as pure energy.
• There cannot be energy without matter.

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ENERGY

• We call the energy that is associated with
  motion, Kinetic Energy (KE).
• Under the influence of a net force (?0), a body
  accelerates as positive work is done on it to
  overcome inertia.
• It increases its speed and gains kinetic energy
  in the process.
• Kinetic energy of any object is equal to
• KE ½ mv2

22
ENERGY

• Since energy is the ability to do work, we can
  relate energy and work together by the following
  equation
• Work ?KE
• Work KEfinal - KEinitial
• Units for energy are the same as the units for
  work, Joules (J).
• All forms of energy will be measured in joules.

23
ENERGY

• Example
• A Boeing 747 airliner, weighing 2.2 ? 106 N at
  takeoff, is cruising at a ground speed of 268
  m/s. Compute its kinetic energy.

24
ENERGY

• Example
• If 1 kg of TNT yields 4.6 ? 106 J, how much TNT
  is the planes KE equivalent to?
• The atom bomb dropped on Hiroshima in 1945
  delivered the energy of about 12.5 kilotons of
  TNT, where 1 kiloton 4 ? 1012 J.

25
ENERGY

• Example
• How much KE does a person have if they have a
  mass of 70 kg and a velocity of 8 m/s?
• A 7.00 kg bowling ball moves at 3.0 m/s. How much
  KE does the bowling ball have?
• How fast must a 2.45 g ping-pong ball move in
  order to have the same KE?

26
ENERGY

• Example
• According to the record books, Aleksandr Zass
  (known to his admirers as Samson) would catch a
  104 lb woman fired from a cannon at around 45
  mph. Assuming that Samson brought her to rest
  uniformly in a distance of 1.00 m, compute the
  average force he exerted on our heroine. As a
  guess, take her landing speed to be 8.94 m/s.

27
ENERGY

• Another type of energy is Gravitational Potential
  Energy (GPE).
• GPE is the energy associated with an object due
  to its position relative to the Earth or some
  other gravitational source.
• GPE mgh
• Units Joules
• Since GPE is a result of an objects position, it
  must be measured relative to some zero level.
• When dealing with GPE, only vertical height is
  important.
• The work done raising a mass equals the increase
  in its potential energy.

28
ENERGY

• Example
• A flagpole painter is carrying a 2.00 kg can of
  white paint. She has climbed 10.0 m up the pole
  from its base, where she just finished having
  lunch on the roof of a 30.0 m tall tower. What is
  the increase in GPE of the can as a result of her
  climbing the pole? What is the total increase in
  the cans GPE above the value it had while it sat
  on the ground?

29
ENERGY

• Example
• What is the GPE of a 6.00 kg ball that is located
  0.5 m above the floor?
• What is the change in GPE of a 50.0 kg person who
  climbs a flight of stairs with a height of 3.0 m
  and a horizontal extent of 5.0 m?

30
ENERGY

• Another type of energy is Mechanical Energy (ME).
• ME is the sum of kinetic energy and all forms of
  potential energy.
• ME KE GPE
• Units Joules
• Law of Conservation of Energy maintains that
  energy can be transformed, but it can neither be
  created or destroyed.

31
ENERGY

• Consider the following
• A ball being tossed into the air
• As the ball rises, what happens to its KE?
• Where does the KE go?
• As the ball returns to Earth, what happens to its
  KE?
• What happens to the ME during the entire trip?
• At every instant in the motion, the total
  mechanical energy is constant if the bodys KE
  increases, its GPE must decrease and vice-versa.

32
ENERGY

• Example
• If we release a pendulum bob with a mass of 1.0
  kg from a height of 1.0 m, what is the pendulums
  GPE before it is released?
• What is its ME?
• What is the pendulums KE at the bottom of its
  swing?

33
ENERGY

• Example
• Starting from rest, a child zooms down a
  frictionless slide with an initial height of 3.00
  m. What is her speed at the bottom of the slide?
  Assume that she has a mass of 25.0 kg.

34
ENERGY

• Example
• A vaulter carrying a graphite-fiberglass pole is
  about to make a jump. At what speed must he run
  in order to clear the 20.0 ft mark? Neglect all
  possible energy losses, take his center to be
  1.00 m above the floor while standing, and
  presume that he just clears the bar?

35
ENERGY

• Example
• A 60 kg skier starts from rest at the top of a 60
  m high slope. She descends without using her
  poles. What is her GPE with respect to the level
  ground at the bottom? Assume friction is
  negligible and compute at what speed she will
  ideally arrive at the bottom.
• Now if she reaches the bottom of the run,
  traveling 25 m/s, what is the net energy
  transferred via friction (i.e. lost to warming
  her, the skis, the slope, and the air)?

36
power

• Power is the rate at which energy is transferred
  into or out of a system.
• Power ?Work/?Time
• P ?W/?t
• James Watt found that a large draft horse could
  exert a pull of about 150 lbs while walking at
  about 2.5 mph for a considerable amount of time.
• That rate is equivalent to 33 000 ft?lbs per
  minute or 550 ft?lb/sec, which is called 1
  horsepower (hp).
• In SI, the unit of power is the watt (W), equal
  to 1 joule of work done per 1 second (1 W 1
  J/s).
• Since a watt is a fairly small amount of power,
  the more convenient kilowatt (1000 watts) is used.

37
power

• Example
• The express elevator in the Sears Tower in
  Chicago averages a speed of 9.144 m/s in its
  climb to the 103rd floor, 408.4 m above the
  ground. Assuming a load of 1.0 ? 103 kg, what
  average power must the lifting motor supply?

38
power

• When a constant force acts on a body that, in the
  process, moves through a distance, an amount of
  work is done (W Fcos? d).
• If this occurs in a time interval,
• Power (Fcos?)(d/t)
• P (Fcos?)vav
• The power delivered to a moving object equals the
  product of the component of the force in the
  direction of the motion and the speed.

39
power

• Example
• In 1935, R.H. Goddard, the American rocket
  pioneer, launched several S-series sounding
  rockets. Given that the engine had a constant
  thrust of 889.6 N, how much power did is transfer
  to the rocket while traveling at its maximum
  speed of 1130 km/hr?

40
power

• This makes it clear that exerting the same force
  on an object thats moving increasingly rapidly
  requires the application of a proportionately
  greater amount of power.
• Its easy to accelerate when jogging at 1 mph,
  but its a lot harder to attain the same
  acceleration when youre already running at 10
  mph.

41
power