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Energy and Work

Explore the concept of energy and work, learn the mathematical proof of work-energy theorem, understand units of energy and work, discover how to find work from a graph, and explore the concept of power. Calculate power in watts and kilowatts with a practical example.

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Energy and Work

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  1. Energy and Work

  2. Energy • Energy – the ability to produce a change in itself or the environment. • If an objects position is changing, that may indicate that it has energy. • Energy due to an objects motion is called Kinetic Energy

  3. Kinetic Energy and Work • KE = ½ mv2 • Energy is a scalar number. There is no direction associated with energy. • Work is defined as a process changing the energy in a system. Work is a vector. • W = Fd • ∆KE = W • This is called the Work-Energy Theorem

  4. Mathematical Proof • vf2 = vi2 + 2ad • F=ma or a = F/m substitute for a • vf2 - vi2 = 2Fd/m • Multiply each side by 1/2m • ½mvf2 - ½mvi2 = Fd • KEf – KEi = W Or ∆KE = W • Units of Energy and Work are Nm or kgm2/s2 or Joules (J)

  5. Work • An agent in the environment exerts a force that displaces an object a distance and changes the amount of energy that object has. • If work goes in to the system W is + and energy If the system does work on the environment W is – and energy of the system

  6. Work cont’d • Work only happens when force and displacement are occurring in the same direction. • Why does a planet in a circular orbit not have any work done to it? • If the force is at an angle to the direction of displacement, you must find the component of force in the same direction as the displacement.

  7. Work Clip • Assume he lifts the weight .3m how much work did he do? (2.2lbs/kg) • How much work does this guy do? • http://www.youtube.com/watch?v=cSJCDcAKShA&feature=related

  8. Finding Work from a Graph • Since W=Fd • Finding the area under a force vs distance graph will give the work done by that force. • This is especially helpful if the magnitude of the force is changing.

  9. Power • Power is the rate of doing work. • Lifting an entire box of books onto a shelf may take two seconds, lifting each book up on the shelf may take 20 minutes. The same amount of work is done but the power is different. • P = W/t • Units are J/s or Watts (W) • A watt is fairly small so many things are measured in kilowatts kW (1000W)

  10. Power Practice • An electric motor lifts an elevator 9.00m in 15.0s by exerting an upward force of 1.20x104N. What power does the motor produce in watts and kilowatts? • W = Fd W = (1.20x104N)(9.00m) • W=10.8x106J • P = W/t P = 10.8x106/15.0s • P=7.2x103W or 7.2 kW

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