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Work & Energy

1. Work & Energy. m. F. ∆x. ∆x. F. m. Fcos θ. Work & Energy. W = F ∆x. W = Dot product of F times ∆x. θ. W = F . ∆x. W = (Fcos θ ) ∆x. Only the component of F parallel to ∆x does work. Fcos θ does do work. The component of F perpendicular to ∆x does no work.

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Work & Energy

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  1. 1 Work & Energy

  2. m F ∆x ∆x F m Fcosθ Work & Energy W = F ∆x W = Dot product of F times ∆x θ W = F . ∆x W = (Fcosθ) ∆x Only the component of F parallel to ∆x does work. Fcosθ does do work. The component of F perpendicular to ∆x does no work. Fsinθ does not do work.

  3. m v Kinetic Energy Kinetic Energy = ½ mass x (velocity)2 KE = ½ mv2 Mass is measured in kilograms velocity is measured in meters/second. Kinetic Energy is measured in Joules.

  4. h F Potential Energy Potential Energy (PE) is stored energy Gravitational Potential Energy (PE)f = mgh W = F d W = mgh PE = mgh (PE)i = 0 PE can be arbitrarily made 0 at any height h

  5. A h B v Gravitational Potential Energy & Kinetic Energy (PE)A = mgh (KE)A = 0 (PE)B = 0 (KE)B = ½ mv2 (PE)A + (KE)A = (PE)B + (KE)B (PE)A = (KE)B

  6. Types of Energy Conservation of Energy E’ = KE’ + PE’ + TE’ KE = Kinetic Energy E = KE + PE + TE PE = Potential Energy TE = Thermal Energy E’ = E KE’ + PE’ + TE’ = KE + PE + TE Energy is defined as the ability to do work. Energy is a scalar. The unit of Work and Energy is the Joule (J). 1J = 1Nm

  7. A h B v (PE)A = mgh (KE)A = 0 Conservative Gravitational Field (PE)B = 0 (KE)B = ½ mv2 (PE)A + (KE)A = (PE)B + (KE)B (PE)A = (KE)B mgh = ½ mv2 v = (2gh)1/2 v = 4.4(h)1/2

  8. h v A (PE)A = mgh (KE)A = 0 Sample Problem 1 (PE)B = 0 (KE)B = ½ mv2 (PE)A = (KE)B B mgh = ½ mv2 v = (2gh)1/2 v = [(2)9.8)(4.0)]1/2 v = 8.8 m/s h = 4.0 m v = ?

  9. ve Escape Velocity v∞ = 0 ve= (2Gmx/Rx)1/2 Escape velocity from any mass mx

  10. ve Escape Velocity from the Earth mE = 5.98 x 1024 kg RE = 6.37 x 106 m G = 6.67 x 10-11 Nm2/kg2 ve= (2GmE/RE)1/2 ve= [(2) 6.67 x 10-11 Nm2/kg2 )(5.98 x 1024 kg)/ 6.37 x 106 m)]1/2 ve= 1.12 x 104 m/s ve= 11,200 m/s ve= 25,000 mi/hr From the Moon ve= 5,400 mi/h From Jupiter ve= 134,000 mi/h

  11. ve Escape Velocity & Black Holes If ve  c, Nothing will escape The mass will be a Black Hole What would be the radius of the Earth that would make it a Black Hole? c= (2GmE/RE)1/2 c2 = (2GmE/RE) RE = 2GmE/c2 RE = 2( 6.67 x 10-11 )(5.98 x 1024 )/(3 x 108)2 RE = 8.9 x 10-3 m RE = .89 cm RE 1 cm

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