Energy, Work and Power

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Energy, Work and Power
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HOMEWORK QUESTION

• Please do this question and hand it by Tuesday
  after the reading week, in class
• A 50kg child slides down a 45o frictionless hill
  for 60m, starting with an initial velocity of
  2m/s. The child then slides for 10m over a flat
  surface that has a coefficient of kinetic
  friction of 0.15, and finally back up another
  frictionless hill with a slope of 30o.
• Draw a pictures of the problem and determine how
  far on the 2nd hill the child ends up (not the
  height).

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For every conservative force, we can define a
potential energy function U so that WAB -DU
UA -UB
Note the negative
Examples Gravity (uniform g) Ug mgy,
where y is height Gravity (exact, for two
particles, a distance r apart)
Ug - GMm/r, where M and m are the masses
Ideal spring Us ½ kx2, where x is the
stretch Electrostatic forces (Fkq1q2/r),
where q are the charges
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Conservation of mechanical energy
If only conservative forces do work, potential
energy is converted into kinetic energy or vice
versa, leaving the total constant. Define the
mechanical energy E as the sum of kinetic and
potential energy
E ? K U K Ug Us ...
Conservative forces only W -DU Work-energy
theorem W DK So, DKDU 0 which
means that E does not change with time.

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Example Pendulum
L

• The pendulum is released from rest with the
  string horizontal.
• Find the speed at the lowest point (in terms of
  the length L of the string).

vf
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Example Pendulum
?

• The pendulum is released from rest at an angle ?
  to the vertical.
• Find the speed at the lowest point (in terms of
  the length L of the string).

vf
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Example

• You slide 20m down a frictionless hill with a
  slope of 30o starting from rest. At the bottom
  you collide and stick to another person (at rest)
  that has 90 of your mass.a) Determine the
  final velocity of the system.b) How would the
  calculation and final velocity change if the
  slope had a coefficient of kinetic friction of
  0.1 ?

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Power

• The time rate of doing work is called power.If
  an external force is applied to an object, and if
  work is done by this force in a time interval ?t,
  the average power is defined as
  PW/?t (unit J/s Watt, W) For
  instantaneous power, we would use the
  derivative
  PdW/dtAnd since WF.s, dW/dtFds/dtF.v, so
  sometimes it is useful to write
  PF . v

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Example

• An elevator motor delivers a constant force of
  2x105N over a period of 10s as the elevator moves
  20m. What is the power ?PW/t Fs/t
  (2x105N)(20m)/(10s) 4x105 W
• The same elevator is moving with an average
  velocity of
• The power is