Lecture 6: Potential Energy

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Lecture 6Potential Energy

• Phys 2101
• Gabriela González

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Power

• Power due to a force time rate at which work is
  done by the force.
• Average power total amount of work done in some
  time ?t, divided by time ?t PavgW/ ?t
• Units PW/tJoule/secWatt
• Another common unit horsepower 1hp 746 W
• What is kW-hr a unit of?

for constant forces!
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Power

• In the Z4, BMW has the Boxster beater it was
  looking for when people realized the Z3 was a
  Miata challenger. Cheaper than the Boxster, I'd
  argue that the Z4 is more of a BMW than the
  Boxster is a true Porsche.There are two engines,
  two transmissions (the SMG paddle-shifted gearbox
  is on the way) and a good chance of breaking 140
  mph in all of them, if youre inclined. Zero to
  60 in the 184-hp, 2.5-liter in-line six comes in
  7.1 seconds, while the 225-hp 3.0-liter gets you
  there in 5.9 seconds. That's in manual
  transmission. Add a second for the automatic
  transmissions for both. The base price of the
  3.0-liter is 40,945, while the 2.5-liter starts
  at 33,795. Save appropriately.
• Car reviews http//www.bullz-eye.com/carreviews/
  2003/bmw_z4.htm

The Z4 has a weight of 3,000 lbs. What is the
average power exerted by a horizontal force to
bring a particle with the same weight from rest
to 60mph in 6 seconds? Whats the instantaneous
power delivered by the engine when the particle
is moving at 60mph?
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Potential energy

• When a conservative force does work W on an
  object, it changes the amount of potential energy
  of that object by

• If the force is constant, W Fd and ?U??Fd.
• If the force is the gravitational force during
  vertical motion, then ?U?mg(yf-yi)mg?y (with
  y-axis pointing up) if particle goes up, Wglt0
  and ?Ugt0.
• If the object is moving horizontally and
  vertically (projectile motion), the potential
  energy is still ?U?mg?y only the vertical
  motion matters.

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Potential energy projectile motion

• When the projectile hits the ground
• Is the work done by gravity positive or
  negative?
• Is the change in potential energy positive or
  negative?
• Is the kinetic energy the same, larger or
  smaller than initially?
• What is the difference in the sum of kinetic and
  potential energy between initial and final points?

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Potential energy springs

• The spring does work on a mass attached to its
  end there is energy transferred from the spring
  to the mass, and converted into kinetic energy.

v
F
spring does negative work, kinetic energy
decreases, mass is slowing down
v
spring does positive work, kinetic energy
increases, mass is speeding up
F
HRW simulation
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Potential energy springs

• Potential energy in the mass due to the work of
  spring, when the mass is at position x

If we choose as initial position the origin,
where the spring is relaxed, then U½ k x2. Work
energy theorem
Conservation of energy!
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Conservation of energy

• If only conservative forces are in action
  (gravity, springs,) then the mechanical energy,
  the sum of potential and kinetic energy, is
  conserved.
• maximum kinetic minimum potential
• minimum kinetic maximum potential