Kinetic and Potential Energy

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Kinetic and Potential Energy

• Conservation of Energy

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Kinetic Energy

• kinetic energy - the energy objects have because
  they are in motion
• m mass of object (kg)
• v velocity of object (m/s)
• Like work, the unit of energy is the
• joule (J)

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Example

• A 1400 kg car is travelling at 30 m/s. What is
  its kinetic energy?

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Work-Energy Theorem

• An important relationship can be found between
  work and kinetic energy. It is known as the
  work-energy theorem,
• the change in an object's kinetic energy is
  equal to the net work done on the object.

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Example

• pool cue strikes a ball of mass 0.25 kg and gives
  it a speed of 1.5 m/s. If the force exerted by
  the cue is 20 N, over what distance did this
  force act?

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Example 2

• A soccer player kicks a soccer ball initially at
  rest. She exerts a force of 500 N on the ball
  over a distance of 10 cm. If the ball has a mass
  of 450 kg, with what speed does it leave her foot?

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Potential Energy

• Potential energy - energy an object has because
  of its position or state. (stored work)
• Use the symbol U to represent potential energy.
• A battery contains chemical potential energy and
  when that energy is released, it can do work to
  power your walkman, etc.

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Gravitational Potential Energy

• The potential energy used most often in physics
  is gravitational potential energy. When you lift
  a bowling ball, you must do work against gravity.
  That work is transformed into gravitational
  potential energy which can be released as kinetic
  energy if you drop the ball.

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Formula for PE

• To eliminate the choosing of a reference point we
  talk about change in potential energy

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Example

• What is the increase in the gravitational energy
  of a 5 kg book that is lifted from the floor to a
  table 1.5 m high?

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Example 2

• A falling ball of mass 250 g losses 25 J of
  gravitational potential energy. What distance has
  the ball fallen?

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Potential Energy of a Spring

• You can also store potential energy in a spring.
  The formula for this is
• Us ½kx2
• Notice that it's the same formula as the work
  done by a spring. Also notice that spring
  potential energy is always positive.

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Example

• A spring has a spring constant of 800 N/m. How
  much must this string be stretched to store 75 J
  of potential energy?

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Displacement and PE
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Energy and Conservation

• One of the most fundamental and powerful ideas in
  physics is the one of energy conservation.
• the total mechanical energy of a system is
  conserved. That is, the energy it initially has
  must be equal to its final energy.
• mechanical energy-the sum of its kinetic and
  potential energies.

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Energy Conservation

• You can write the conservation of energy
  statement in many different mathematical forms.
  Here are some of them
• KEi PEi KEf PEf

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Example

• A biologist uses a spring-loaded gun to shoot
  tranquilizer darts into a wild African hamster.
  The spring in the gun has a spring constant of
  940 N/m. A 38 g dart is loaded into the gun and
  the spring is compressed a distance of 25 cm.
  With what speed will the dart leave the gun?