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Physics 121

Physics 121 6. Work and Energy 6.1 Work 6.3 Kinetic Energy 6.4 Potential Energy 6.5 Conservative and Non-conservative forces 6.6 Mechanical Energy / Problem Solving 6.8 Conservation of Energy 6.9 Dissipative Forces / Problem Solving 6.10 Power Work

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Physics 121

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  1. Physics 121

  2. 6.Work and Energy 6.1 Work 6.3 Kinetic Energy 6.4 Potential Energy 6.5 Conservative and Non-conservative forces 6.6 Mechanical Energy / Problem Solving 6.8 Conservation of Energy 6.9 Dissipative Forces / Problem Solving 6.10 Power

  3. Work Work = Force x Distance W = F . d

  4. 200 N Example 6.1 . . . Work for Slackers! You push a car with a force of 200 N over a distance of 3 m. How much work did you do?

  5. Solution 6.1 . . . Work for Slackers! W = F.d W = 200x3 W = 600 Nm W = 600 J Note: A Joule (J) is just another term for newton . meter (N m)

  6. Energy Energy is the capacity to do work Kinetic Energy (motion) Potential Energy (position)

  7. Kinetic Energy K.E. = 1/2mv2

  8. Example 6.2 . . . Kinetic Energy The K.E. of a car is 600 J and its mass is 1000 kg. What is its speed?

  9. Solution 6.2 . . . Kinetic Energy K.E. = 1/2 m v2 600 = 1/2(1000)(v2) v = 1.1 m/s

  10. Example 6.3 . . . Save your work! You lift a 2 kg book and put it on a shelf 3 meters high. (a) How much work did you do? (b) Was the work “lost”?

  11. Solution 6.3 . . . Save your work! (a) W = F.d W = mgh W = 2x10x3 W = 60 J (b) Work was stored as Potential Energy (hidden). So gravitational P.E. = mgh

  12. 15 m 30 m Example 6.4 . . . Downhill A 65 kg bobsled slides down a smooth (no friction) snow-laden hill. What is its speed at the bottom?

  13. 15 m 30 m Solution 6.4 . . . Downhill P.E. = K.E. mgh = 1/2 mv2 9,555 = (1/2)(65) v2 v = 17.1 m/s

  14. Example 6.5 . . . Sticky bobsled Suppose the speed of the bobsled was actually measured to be 14.8 m/s instead of 17.1 m/s (a) What could have caused that? (b) What was the work done by the bobsled against friction?

  15. Solution 6.5 . . . Sticky bobsled (a) Not all the P.E. was converted to K.E. because some work was lost (heat energy) in doing work against friction: P.E. = K.E. + Wf (b) mgh = 1/2 mv2 + Wf 9,555 = 1/2(65) (14.8)2 + Wf Wf = 2,436 J

  16. Lab Experiment Slope = “k” F x Stretching Springs Hooke’s Law: The amount of stretch is directly proportional to the force applied. F = k x

  17. Example 6.6 . . . Springy Spring The spring constant (k) of a spring is 20 N/m. If you hang a 50 g mass, how much will it stretch?

  18. Lab Experiment Solution 6.6 . . . Springy Spring F = k x mg = kx (50 /1000)(9.8) = (20)(x) x = 2.5 cm

  19. Example 6.7 . . . Body building How much work would you have to do to stretch a stiff spring 30 cm (k = 120 N/m)?

  20. “Solution” 6.7 . . . Body building W = F . d W = (kx)(x) W = kx2 W = (120)(0.3)2 W = 10.8 J X 

  21. Correct Solution 6.7 . . . Body building W = F . d We must use the AVERAGE Force! W = (1/2)(kx)(x) W =1/2 kx2 W = (1/2)(120)(0.3)2 W = 5 .4 J   P.E. of a Spring = 1/2kx2

  22. 40 N 600 10 kg Hawaii or Bust! Example 6.8 . . . Lugging the Luggage What is the speed when the distance is 3 m?

  23. 40 N 600 10 kg Hawaii or Bust! Solution 6.8 . . . Lugging the Luggage What is the speed when the distance is 3 m? F.d = 1/2 m v2 (40 cos 600)(3) = (1/2)(10)(v2) v = 3.5 m/s Moral of the story W = (F)(d)(cos)

  24. Conservative Forces If the work done against a force does not depend on the path taken then that force is called a conservative force. Examples are gravity and spring force. The total mechanical energy (P.E. + K.E.) will remain constant in this case. If the work done against a force depends on the path taken then that force is called a non-conservative force. Example is friction. The total mechanical energy (P.E. + K.E.) will not remain constant in this case. Vote Democrat . . . Just kidding!

  25. Example 6.9 . . . Playing with Power Power is the rate of doing work P = W / t A pump can lift at most 5 kg of water to a height of 4 m every minute. What is the power rating of this pump?

  26. Solution 6.9 . . . Playing with Power W = mgh W = (5)(10)(4) W = 200 J P = W / t P = 200 J / 60 s P = 3.3 J / s P = 3.3 W Note: Watt (W) is just another term for Joules / second (J / s)

  27. That’s all folks!

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