2. 1

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

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

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

6. Gravitational Potential Energy & Kinetic Energy (PE) B = 0 (PE) A = mgh h A v B (KE) A = 0 (KE) B = ½ mv 2 (PE) A + (KE) A = (PE) B + (KE) B (PE) A = (KE) B

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

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

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

10. Escape Velocity veve Escape velocity from any mass m x v e = (2Gm x /R x ) 1/2 v ∞ = 0

11. Escape Velocity from the Earth veve v e = (2Gm E /R E ) 1/2 m E = 5.98 x 10 24 kg R E = 6.37 x 10 6 m G = 6.67 x 10 -11 Nm 2 /kg 2 v e = [(2) 6.67 x 10 -11 Nm 2 /kg 2 )(5.98 x 10 24 kg )/ 6.37 x 10 6 m)] 1/2 v e = 1.12 x 10 4 m/sv e = 25,000 mi/hr From the Moonv e = 5,400 mi/hFrom Jupiterv e = 134,000 mi/h v e = 11,200 m/s

12. Escape Velocity & Black Holes veve If v e  c, Nothing will escape The mass will be aBlack Hole What would be the radius of the Earth that would make it a Black Hole? c = (2Gm E /R E ) 1/2 c 2 = (2Gm E /R E )R E = 2Gm E /c 2 R E = 2( 6.67 x 10 -11 )(5.98 x 10 24 )/(3 x 10 8 ) 2 R E = 8.9 x 10 -3 mR E =.89 cm R E  1 cm