Reading Quiz - Work

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Reading Quiz - Work Energy

• 1. A woman holds a bowling ball in a fixed
  position. The work she does on the ball
• ___ 1. depends on the weight of the ball.
• ___ 2. cannot be calculated without more
• information.
• ___ 3. is equal to zero.

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• 2. A man pushes a very heavy load across a
  horizontal floor. The work done by gravity on the
  load
• ___ 1. depends on the weight of the load.
• ___ 2. cannot be calculated without more
• information.
• ___ 3. is equal to zero.

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• 3. When you do positive work on a particle, its
  kinetic energy
• ___ 1. increases.
• ___ 2. decreases.
• ___ 3. remains the same.
• ___ 4. need more information about the way
• the work was done

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• 4. The gravitational potential energy of a
  particle at a height z above Earths surface
• ___ 1. depends on the height z.
• ___ 2. depends on the path taken to bring the
  
• particle to z.
• ___ 3. both 1 and 2.
• ___ 4. is not covered in the reading assignment.

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• 5. Which of the following is not a conservative
  force?
• ___ 1. the force exerted by a spring on a
• particle in one dimension
• ___ 2. the force of friction
• ___ 3. the force of gravity
• ___ 4. not covered in the reading assignment

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Work

• Work done by a constant force on an
  object where F magnitude of constant
  force d magnitude of the displacement ?
  angle between the force and displacement
  vectors

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• Graphical interpretation of work
• Work done by a variable force.

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Conceptual Questions

• 1) A box slides through a distance of 3 m on a
  rough floor where the force of friction is 10 N.
  What is the work done on the box?
• ____ a) 0 Nm
• ____ b) 30 Nm
• ____ c) - 30 Nm
• ____ d) 0.30 Nm
• ____ e) - 0.30 Nm

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• 2) The moon revolves around the earth in a
  circular orbit, kept there by the gravitational
  force exerted by the earth. Gravity does
• ___ a) positive work
• ___ b) negative work
• ___ c) no work
• ___ d) variable work
• on the moon.
• What evidence do you have to support your answer?

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• 3) The figure shows four situations in which a
  force acts on a box while the box slides to the
  right a distance d across a frictionless floor.
  The magnitudes of the forces are identical. Rank
  the situations according to the work done on the
  box during the displacement, from most positive
  to most negative.

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Quantitative Questions

• 1) Find the work done by the force of gravity
  when an object of mass m is raised from a height
  of y meters to a height of yh meters.
• 2) A spring is a device where the force it exerts
  is directly proportional to its displacement from
  its natural (unstretched) length. The constant of
  proportionality is called the spring constant k.
  Draw a graph of the spring force versus its
  displacement. What is the work done in stretching
  a spring from its natural length by an amount x?

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• 3) A 280 kg piano slides 4.3 m down a 30? incline
  and is kept from accelerating by a man who is
  pushing back on it parallel to the incline. The
  effective coefficient of kinetic friction is
  0.40. Calculate (a) the force exerted by the
  man, (b) the work done by the man on the piano,
  (c) the work done by the friction force, (d) the
  work done by the force of gravity, and (e) the
  net work done on the piano.

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Energy

• Energy - property that gives something the
  capacity to do work. Three broad categories -
  Kinetic energy - Potential energy - Rest
  energy
• Kinetic Energy - Energy related to motion
  (definition)
• Potential Energy - Energy related to position.
• Rest Energy - Energy by virtue of the mass of an
  object

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Work-Energy Principle

• The net work done on an object is always equal to
  the change in its kinetic energy
• Conservative forces work done by these forces
  are independent of path they depend only on the
  end points. Examples include gravitation, spring
  and magnetic forces.
• It is meaningful to define an associated
  potential energy only for conservative forces.

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Quantitative Problems

• 1) An automobile traveling 60 km/h can brake to a
  stop within a distance of 20 m. If the car is
  going twice as fast, 120 km/h, what is its
  stopping distance? The maximum braking force is
  approximately independent of speed.
• 2) A 600 gram hammer head strikes a nail at a
  speed of 4.0 m/s and drives it 5.0 mm into a
  wooden board. What is the average force on the
  nail?

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• 3) A crate of mass 10 kg is pulled up a rough
  incline with an initial speed of 1.5 m/s. The
  pulling force is 100 N parallel to the incline,
  which makes an angle of 20 with the horizontal.
  If the coefficient of kinetic friction is 0.4,
  and the crate is pulled a distance of 5 m, (a)
  how much work is done against gravity? (b) How
  much work is done against friction? (c) How much
  work is done by the 100 N force? (d) What is the
  change in kinetic energy of the crate? (e) What
  is the speed of the crate after being pulled 5 m?

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Potential Energy

• For every conservative force, we can define a
  potential energy function. The change in the
  potential energy is equal to the negative of the
  work done by the conservative force
• Examples gravitational PE mgh elastic
  PE
• Note Cannot define a potential energy function
  for a non-conservative force.

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Conservation of Mechanical Energy

• Net work done by net force which equals the
  vector sum of conservative and non-conservative
  forces, implying
• Since , and , the above reduces to
  - the general form of the work-energy principle.
• If only conservative forces are acting, or if the
  work done by the non-conservative forces present
  is zero, i.e. , then

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Conceptual Question

• Two water slides at a pool are shaped
  differently but start at the same height h. Two
  riders, Paul and Kathleen, start from rest at the
  same time on different slides.

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• Which rider, Paul or Kathleen, is travelling
  faster at the bottom and who gets there first?
• ___ a) Paul Paul ___ e) same Paul
• ___ b) Paul Kathleen ___ f) same Kathleen
• ___ c) Kathleen Paul ___ g) Paul same
• ___ d) Kathleen Kathleen ___ h) Kathleen same

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Quantitative Problems

• 1) A small mass m slides without friction along
  the looped apparatus show. If the object is to
  remain on the track, even at the top of the
  circle (whose radius is r), from what minimum
  height h must it be released?

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• 2) A roller coaster is pulled up to point A where
  it is released from rest. Assuming no friction,
  calculate the speed at points B, C and D. Now
  suppose the roller coaster passes point A with a
  speed of 1.70 m/s. If the average force of
  friction is equal to one fifth of its weight,
  with what speed will it reach point B? The
  distance traveled is 45.0 m.

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• 3) A ball is attached to a horizontal cord of
  length L whose other end is fixed. (a) If the
  ball is released, what will be its speed at the
  lowest point of its path? (b) A peg is located a
  distance h directly below the point of attachment
  of the cord. If h 0.80L, what will be the speed
  of the ball when it reaches the top of its
  circular path about the peg?

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• 4) The figure shows an 8 kg stone at rest on a
  spring. The spring is compressed 10.0 cm by the
  stone. (a) What is the spring constant? (b) The
  stone is pushed down an additional 30.0 cm and
  released. What is the elastic potential energy of
  the compressed spring just before that release?

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• (c) What is the change in the gravitational
  potential energy of the stone-Earth system when
  the stone moves from the release point to its
  maximum height? (d) What is that maximum height,
  measured from the release point?

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Conservation of Energy Power

• The law of conservation of energy is one of the
  most important principles of physics. It
  states The total energy is neither increased
  nor decreased in any process. Energy can
  be transformed from one form to another, and
  transferred from one body to another, but the
  total amount remains constant.
• Power rate of doing work (or transforming
  energy). Hence average power is

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Discussion Problems

• 1) Other than nuclear energy, why do we say the
  source of all energy comes from the sun?
  Specifically, what about
• (a) wind energy
• (b) hydro-electricity
• (c) fossil fuel - coal, wood, oil, gas
• (d) food that we eat

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• 2) To accelerate your car at a constant
  acceleration, the cars engine must
• ____ a) maintain a constant power output
• ____ b) develop ever-decreasing power
• ____ c) develop ever-increasing power
• ____ d) maintain a constant turning speed

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• 3) Compared to yesterday, you did 3 times the
  work in one-third the time. To do so, your power
  output must have been
• ____ a) the same as yesterdays power output
• ____ b) one-third of yesterdays power output
• ____ c) 3 times yesterdays power output
• ____ d) 9 times yesterdays power output