Lecture 5: Work, energy, power Examples

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Lecture 5Work, energy, powerExamples

• Phys 2101
• Gabriela González

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Ch 7 Kinetic Energy and Work
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Work-Energy Theorem example

• A constant force moves a body with mass 3kg a
  distance of 2 meters in 2 seconds, starting from
  rest.
• What is the magnitude of the force?
• Whats the work the force did on the mass?
• Use the work-energy theorem to calculate the
  velocity of the mass at t2s.

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Work-Energy theorem

• A variable force F acts along the x-axis on a
  10kg mass. The particle starts at rest at x0.
• Where is the particle when it has the greatest
  kinetic energy?
• Where is the particle when it has the smallest
  kinetic energy?
• Whats the particle direction of travel after it
  reaches x1, 3, 5, 6m?

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Example

• Two blocks are connected over a pulley. The mass
  of block A is 10 kg, and the coefficient of
  kinetic friction between A and the incline is
  ?k0.20. Angle ? of the incline is 30. Block A
  slides down the incline at constant speed.
• What is the mass of block B?
• What is the tension force?
• What is the work done by gravity on the system
  when the mass B moves up by 20cm?
• What is the work done by friction on block A
  during the same interval?

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Example

• A 250 g block is dropped onto a relaxed vertical
  spring with k2.5 N/cm. The block becomes
  attached to the spring and compresses the spring
  12 cm before momentarily stopping.

• While the spring is being compressed, what work
  is done on the block by the gravitational force?
• And by the spring force?
• Whats the blocks speed just before it hits the
  spring?

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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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Example

• What is the magnitude of the force F you must
  exert to move the canister at a constant speed?
• How far must you pull the free end of the cord to
  move the canister up by a distance d?
• During that lift, what is the work done on the
  canister done by
• your force?
• the gravitational force?