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Exploring Kinetic Energy and Power in Mechanics

Dive into the effects of mass and velocity on kinetic energy, types of mechanical energy, conservation principles, energy calculations, and power in mechanical systems.

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Exploring Kinetic Energy and Power in Mechanics

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  1. Chapter 5.3 Review

  2. 1. What has a greater effect on kinetic energy, changing mass or changing velocity? Why?

  3. Changing velocity, because it is squared in the equation.KE = ½ mv2

  4. 2. List the types of energy that make up mechanical energy.

  5. Gravitational potential energy, elastic potential energy, and kinetic energy.

  6. 3. What does it mean when we say mechanical energy is conserved?

  7. The total amount of mechanical energy remains the same. It can change from one type of mechanical energy to another, but the total amount remains the same.

  8. 4. A spring of spring constant 100 N/m is compressed 0.1 m. A ball of mass 0.030 kg is placed on top of the spring, and the spring is released. What is the maximum height the ball reaches?

  9. PEg = PEemgh = ½ kx2(.03)10h = ½(100)0.12h = 1.67 m

  10. 5. When the ball in question 4 falls back to earth, what is its velocity when it hits the ground?

  11. PE = KEmgh = ½ mv2(0.03)10(1.67) = ½ 0.03v2v = 5.8 m/s

  12. 6. A car on a roller coaster tops a hill at a speed of 5 m/s. The hill is 100 m in height. What is the speed of the car at the bottom of the hill?

  13. PE + KE0 = KEfmgh + ½ mv02 = ½ mvf2gh + ½v02 = ½vf210(100) + ½(5)2 = ½vf2vf = 45 m/s

  14. 7. I pick up 20 books, one at a time, and set them on a table. You pick up all 20 books at once and set them on the table. Which one of us did the most work? Which one of us expended the most power?

  15. The amount of work was the same. You expended more power because the work was done faster.

  16. 8. What does the power rating of a machine indicate about its rate of energy production?

  17. The power rating IS the rate of energy production!

  18. 9. What are the two formulas for calculating power?

  19. P = W/tP = Fv

  20. 10. A 60 kg firefighter climbs a 20 m ladder in 40 seconds. How much work did the firefighter do? How much power was expended by the firefighter?

  21. W = FdW = mghW = 60(10)20W = 12000 JP = W/tP = 12000/40P = 300 watts

  22. 11. A 500 kg motorcycle accelerates from rest to a speed of 25 m/s in 15 seconds. What is the average power produced by the engine of the motorcycle?

  23. F = maF = 500(25/15) = 833 Nd = ½ at2d = ½ (25/15)(15)2 = 187.5P = Fd/tP = 833(187.5)/15P = 10400 W

  24. OR P = FvThe force is still 833 N, v is the average velocity 25/2 = 12.5 m/s.P = 833 x 12.5 m/sP = 10400 W

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