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CONSERVATION OF MECHANICAL ENERGY

CONSERVATION OF MECHANICAL ENERGY. What is Mechanical Energy?. Mechanical Energy. The sum of kinetic energy and all forms of potential energy within a system. Mechanical Energy. The sum of kinetic energy and all forms of potential energy “ME” ME = KE + PE.

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CONSERVATION OF MECHANICAL ENERGY

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  1. CONSERVATION OF MECHANICAL ENERGY What is Mechanical Energy?

  2. Mechanical Energy • The sum of kinetic energy and all forms of potential energy within a system.

  3. Mechanical Energy • The sum of kinetic energy and all forms of potential energy • “ME” • ME = KE + PE

  4. Conservation of Mechanical Energy • Conserved means stays constant • The law is MEi = MEf or Initial mechanical energy = Final mechanical energy (in the absence of friction)

  5. Conservation of Mechanical Energy • Another way to write the law is MEi = MEf Or 0.5 mvi2 + mghi = 0.5 mvf2 + mghf

  6. Conservation of Mechanical Energy • Example 1 Starting from rest, a child zooms down a frictionless slide with an initial height of 3.00m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg. Here is the formula – you try it first: 0.5 mvi2 + mghi = 0.5 mvf2 + mghf

  7. Conservation of Mechanical Energy • Example 1 Starting from rest, a child zooms down a frictionless slide with an initial height of 3.00m. What is her speed at the bottom of the slide? Assume she has a mass of 25.0 kg. Here is the formula – you try it first: 0.5 mvi2 + mghi = 0.5 mvf2 + mghf 0.5 (25kg)(0) + 25kg(9.8m/s2)(3m) = 0.5 (25kg)vf2 + 25kg(9.8m/s2)(0 m) 0 + 735J = 12.5 vf2 + 0 7.67m/s = vf

  8. Conservation of Mechanical Energy • Example 2 A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 200 N/m. a. What is the elastic PE of the slingshot before it is released?

  9. Conservation of Mechanical Energy • Example 2 A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 200 N/m. a. What is the elastic PE of the slingshot before it is released? PEi = 0.5 kx2 = 0.5 (200N/m)(.06m)2 = .36J

  10. Conservation of Mechanical Energy • Example 2 A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 200 N/m. a. What is the elastic PE of the slingshot before it is released? PEi = 0.5 kx2 = ½ (200N/m)(.06m)2 = .36J b. What is the KE of the ball just after the slingshot is released?

  11. Conservation of Mechanical Energy • Example 2 A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 200 N/m. a. What is the elastic PE of the slingshot before it is released? PEi = 0.5 kx2 = ½ (200N/m)(.06m)2 = .36J b. What is the KE of the ball just after the slingshot is released? KEf = same as PEi = .36J, all the initial PE was converted to the final KE

  12. Conservation of Mechanical Energy • Example 2 continued c. What is the ball’s speed at the instant it is released?

  13. Conservation of Mechanical Energy • Example 2 continued c. What is the ball’s speed at the instant it is released? KEf = 0.5 mv2 .36J = 0.5 (10.0kg)v2 8.5m/s = v

  14. Conservation of Mechanical Energy • Video Clip: http://www.youtube.com/watch?v=JLyWacUfTYY

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