Chapter 7. Kinetic Energy and Work

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Chapter 7. Kinetic Energy and Work

• 7.1. What is Physics?      
• 7.2. What Is Energy?      
• 7.3. Kinetic Energy      
• 7.4. Work      
• 7.5. Work and Kinetic Energy      
• 7.6. Work Done by the Gravitational Force      
• 7.7. Work Done by a Spring Force      
• 7.8. Work Done by a General Variable Force      
• 7.9. Power

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What is Physics?  
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Kinetic Energy

• Kinetic energy K is energy associated with the
  state of motion of an object.

For an object of mass m whose speed v is well
below the speed of light, Kinetic energy K is
Unit for Kinetic energy is
Kinetic energy is a scalar quantity.
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Work

• Work W is energy transferred to or from an
  object by means of a force acting on the object.
• Energy transferred to the object is positive
  work,
• Energy transferred from the object is negative
  work.

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Finding an Expression for Work
                                                                                                                                    

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Properties of Work

• Only the force component along the objects
  displacement will contribute to work.
• The force component perpendicular to the
  displacement does zero work.
• A force does positive work when it has a vector
  component in the same direction displacement,
• A force does negative work when it has a vector
  component in the opposite direction.
• Work is a scalar quantity.

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Conceptual Example

• The figure shows four situations in which a
  force acts on a box while the box slides
  rightward a distance across a frictionless floor.
  The magnitudes of the forces are identical their
  orientations are as shown. Rank the situations
  according to the work done on the box by the
  force during the displacement, from most positive
  to most negative.

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Question

• A shopping bag is hanging straight down from
  your hand as you walk across a horizontal floor
  at a constant velocity.
• Does the force that your hand exerts on the bags
  handle do any work? Explain.
• Does this force do any work while you are riding
  up an escalator at a constant velocity? Give a
  reason for your answer.

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Example

• During a storm, a crate of crepe is sliding
  across a slick, oily parking lot through a
  displacement
• while a steady wind
  pushes against the crate with a force
  . The situation and coordinate
  axes are shown in Fig. 7-5. How much work does
  this force do on the crate during the
  displacement?

                           .
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Work Done by Variable Forces
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Work Done by a Three-Dimensional Variable Force

• The infinitesimal amount of work dW done on
  the particle by the force is

The work W done by while the particle moves from an initial position with coordinates (x1, y1, z1) to a final position with coordinates (x2, y2, z2) is then

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Net WorkKinetic Energy Theorem

• When a net external force does work Wnet on an
  object, the change of kinetic energy of the
  object equals to the net work

Where
Units of work and energy are 1 joule 1 J 1
kgm2/s2 1 Nm
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Conceptual Example   Work and Kinetic Energy

• Figure illustrates a satellite moving about
  the earth in a circular orbit and in an
  elliptical orbit. The only external force that
  acts on the satellite is the gravitational force.
  For these two orbits, determine whether the
  kinetic energy of the satellite changes during
  the motion.

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EXAMPLE

• A 2.0 kg stone moves along an x axis on a
  horizontal frictionless surface, acted on by only
  a force Fx(x) that varies with the stone's
  position as shown in Fig.
• (a) How much work is done on the stone by the
  force as the stone moves from its initial point
  at x1  0 to x2  5 m?
• (b) The stone starts from rest at x1  0 m. What
  is its speed at x  8 m?

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Checkpoint 1

• A particle moves along an x axis. Does the
  kinetic energy of the particle increase,
  decrease, or remain the same if the particles
  velocity changes
• (a) from -3 m/s to -2 m/s and
• (b) from -2 m/s to 2 m/s?
• (c) In each situation, is the work done on the
  particle positive, negative, or zero?

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EXAMPLE

• During a storm, a crate of crepe is sliding
  across a slick, oily parking lot through a
  displacement while a steady wind
  pushes against the crate with a force
  The situation and coordinate axes are shown in
  Fig.

1. How much work does this force from the wind do on
   the crate during the displacement?
2. If the crate has a kinetic energy of 10 J at the
   beginning of displacement , what is its kinetic
   energy at the end of assuming ?

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Example   Deep Space

• The space probe Deep Space 1 was launched October
  24, 1998. Its mass was 474 kg. The goal of the
  mission was to test a new kind of engine called
  an ion propulsion drive, which generates only a
  weak thrust, but can do so for long periods of
  time using only small amounts of fuel. The
  mission has been spectacularly successful.
  Consider the probe traveling at an initial speed
  of v0275 m/s. No forces act on it except the
  56.0-mN thrust of its engine. This external force
  F is directed parallel to the displacement s of
  magnitude . Determine the final
  speed of the probe, assuming that the mass
  remains nearly constant.

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Example

• Three Forces Figure shows three forces applied
  to a trunk that moves leftward by 3.00 m over a
  frictionless floor. The force magnitudes are
  FA  5.00 N, FB  9.00 N, and FC  3.00 N. During
  the displacement, (a) what is the net work done
  on the trunk by the three forces and (b) does the
  kinetic energy of the trunk increase or decrease?

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Example

• The skateboarder in Figure a is coasting down
  a ramp, and there are three forces acting on her
  her weight W (magnitude675 N), a frictional
  force f (magnitude125 N) that opposes her
  motion, and a normal force FN (magnitude612 N).
  (a) Determine the net work done by the three
  forces when she coasts for a distance of 9.2 m.
  (b) If the skateboards initial speed is zero,
  what will be her final kinetic energy?

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Work Done by the Gravitational Force
Work done on the ball by the gravity is

• If an object is moving down,

• If an object is moving up,

Work done by the gravity only depends on the
change of height, not depends on the path.
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Work Done by a Spring Force

• The spring force given by Hookes Law

The work done by spring force
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Example

•  In Fig., a horizontal force Fa of magnitude
  20.0 N is applied to a 3.00 kg psychology book as
  the book slides a distance d0.500m up a
  frictionless ramp at angle ?30 degrees. (a)
  During the displacement, what is the net work
  done on the book by Fa , the gravitational force
  on the book, and the normal force on the book?
  (b) If the book has zero kinetic energy at the
  start of the displacement, what is its speed at
  the end of the displacement?

                                                                                   

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Example

• The only force acting on a 2.0 kg body as it
  moves along a positive x axis has an x component
  , with x in meters. The velocity at is 8.0 m/s.
  (a) What is the velocity of the body at ? (b) At
  what positive value of x will the body have a
  velocity of 5.0 m/s?

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Power

• The rate at which work is done by a force is
  called the power.

• The average power due to the work done by a force
  during that time interval as

• We define the instantaneous power P as the
  instantaneous rate of doing work, so that

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The units of power
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Sample Problem

• Figure 7-16 shows constant forces F1 and F2
  acting on a box as the box slides rightward
  across a frictionless floor. Force F1 is
  horizontal, with magnitude 2.0 N force F2 is
  angled upward by 60 to the floor and has
  magnitude 4.0 N. The speed v of the box at a
  certain instant is 3.0 m/s. What is the power due
  to each force acting on the box at that instant,
  and what is the net power? Is the net power
  changing at that instant?