Potential Energy and Energy Conservation

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Chapter 7

• Potential Energy and Energy Conservation

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Potential Energy

• Work done by gravity
• Wmg (Y2-Y1)

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Work done moving up

• Work done by hand/normal force against gravity
• Wmg (Y2-Y1)
• (If no acceleration)
• The work by you turns into work by gravity then
  KE

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Potential energy The energy available to do
damage

• Back to swing story
• A 100kg boy swings from a tire swing of
• Length 3m. The angle at the beginning is 53
  degrees.
• a. What is the speed at the bottom?
• b. What is the tension in the string?

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Add Elastic Energy

• As shown last week When x is positive (spring is
  stretched), F is negative
• When x is 0 (at the equilibrium position), F is 0
• When x is negative (spring is compressed), F is
  positive

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Hookes Law

• The force exerted by the spring is always
  directed opposite to the displacement from
  equilibrium
• F is called the restoring force
• If the block is released it will oscillate back
  and forth between x and x

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Work Done by a Spring

• Identify the block as the system
• Calculate the work as the block moves from xi -
  xmax to xf 0
• The total work done as the block moves from
• xmax to xmax is zero

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Spring with an Applied Force

• Suppose an external agent, Fapp, stretches the
  spring
• The applied force is equal and opposite to the
  spring force
• Fapp -Fs -(-kx) kx
• Work done by Fapp is equal to ½ kx2max

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Energy bar diagram, problem 2

• A block of mass m5kg is sliding 11m down a
  frictionless inclined plane, inclination 37
  degrees. It then hits a spring with K800 N/m
  spring constant. How many meters would the spring
  be compressed?

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Instantaneous Power

• The instantaneous power is the limiting value of
  the average power as Dt approaches zero
• This can also be written as

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Units of Power

• The SI unit of power is called the watt
• 1 watt 1 joule / second 1 kg . m2 / s2
• A unit of power in the US Customary system is
  horsepower
• 1 hp 746 W
• Units of power can also be used to express units
  of work or energy
• 1 kWh (1000 W)(3600 s) 3.6 x106 J

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Example

• A 50.0 kg marathon runner runs up the stairs to
  the top of Chicagos 443-m-tall Sears Tower, the
  tallest building in the United States. To lift
  herself to the top in 15 minutes, what must be
  her average power output in watts? In kilowatts?
  In horsepower?

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