Physics 2211a Kulp Class 31: When is energy conserved

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Physics 2211a (Kulp)Class 31 When is energy
conserved?

• W. D. Kulp
• william.kulp at physics.gatech.edu
• Office W501b
• Office Hours MF 11-12 AM, Tu 9-10 AM, by appt.
• www.physics.gatech.edu/academics/Classes/fall200
  6/2211/a/

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Where were we?

• Last class Class 30 (work)

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Where are we?

• Last class Class 30 (work)

• Today Class 31
• Analyze a physical situation using the
  connections among force, work, and energy.
• Determine the change in mechanical energy due to
  a nonconservative force.
• Calculate the force associated with a potential
  energy.

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Conservation of energy

• Energy can be transformed (converted) without
  loss in a system where energy is conserved.

K 0
U mg(2h)
2h
K mgh
h
U mgh
K 2mgh
U 0
0
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Conservative forces

• Move a block from the floor (A) to the table (B).

The work done is independent of the path.

• A potential energy can be associated with any
  conservative force.

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The epitaph of Stevinus

• What weight, w, must be hung from the pulley to
  balance the 10 N block on the ramp?

• Imagine moving the block up to the top of the
  ramp. The weight falls 5 m.

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The net force on the block and weight are the
same when balanced, thus the same work is done on
each and we equate the changes in potential
energy.
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w (5 m) (10 N)(3 m)
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The epitaph of Stevinus

• What weight, w, must be hung from the pulley to
  balance the 10 N block on the ramp?

• Inscribed on the gravestone of (Stevinus) Simon
  Stevin (1548-1620) a Dutch mathematician.

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The hanging weights do not shift, thus the system
is in balance with a weight ratio of 35.
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The principle of virtual work

• What weight, w, must be hung from the pulley to
  balance the weighted platform?

• Imagine the weight falls some distance (say 4
  cm).
• How high do the two weights rise?

8 m
4 m
2 m
60
100
w
The center of the plank goes up 2 cm, while the
100 N bucket rises 1 cm. w(-4) (2)(60)
(1)(100) 55 N
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• A 200 g block on a rough surface with ?k 0.8 is
  pushed against a spring with k 500 N/m,
  compressing the spring 2.0 cm. When released,
  with what speed is the block shot away from the
  spring?

x0
x-2

• v 0.8 m/s

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• A rope with a tension of 33 N pulls a 2.0 kg box
  up a rough (?k 0.3), 2.0-m-long, 30 incline.
  What is the speed of the box at the top? (Assume
  g 10 m/s2)

What forces are nonconservative?
30
0.5
0.866
-20 66 - 10 36

• v 6 m/s

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• The plot below shows the potential energy of a
  particle, due to the force exerted on it by
  another particle, as a function of distance. Of
  the three labeled regions, the magnitude of the
  force on the particle is largest at?

• Region X
• Region Y
• Region Z

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• 4 N
• 2 N
• 1 N
• -1 N
• -2 N
• -4 N

• A particle moves along the x-axis with the
  potential energy shown. What is the x-component
  of the force on the particle when it is at x 4
  m?

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• Pushing a block across a rough table at constant
  speed.

• What objects are included in the system?
• List conservative, nonconservative, external
  forces.
• Specify the sign of ?K, ?U, Wdiss, and Wext.
• Describe energy transformations which occur.
• Describe energy transfers that take place.

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Whats next?

• Monday, 11/6 Class 32 Where does energy go?
• Analyze a situation in which the mechanical
  energy of an object is changed by a dissipative
  force (e.g., friction) or by an external force.
• Calculate the power required to maintain constant
  acceleration of an object.
• Determine the work performed by a force that
  supplies constant power, or the average power
  supplied by a force that performs a specified
  amount of work.

• To-do list
• Homework 30 before class on Monday
• Read assignment (11.7 - 11.9)

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• A cart on an air track is moving at 0.5 m/s when
  the air is suddenly turned off. The cart comes
  to rest after traveling 1 m. The experiment is
  repeated, but now the cart is moving at 1m/s when
  the air is turned off. How far does the cart
  travel before coming to rest?
• 1 m
• 2 m
• 3 m
• 4 m
• 5 m
• Impossible to determine

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• Which of the following is not a conservative
  force?
• the force exerted by a spring on a particle in
  one dimension
• the force of friction
• the force of gravity
• not covered in the reading assignment

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• At the bowling alley, the ball-feeder mechanism
  must exert a force to push the bowling balls up a
  1.0-m long ramp. The ramp leads the balls to a
  chute 0.5 m above the base of the ramp.
  Approximately how much force must be exerted on a
  5.0-kg bowling ball?
• 200 N
• 50 N
• 25 N
• 5.0 N
• impossible to determine

1.0 m
F?
0.5 m