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Work and Energy

Work and Energy. Work = Force X distance W = Fd Unit - Joules (N m), (kg m 2 /s 2 ) Force must be in the direction of the motion. Work and Direction. Lifting a box is work Fighting force of gravity. Lifting force in same direction box moves. Your lifting force and the boxes direction.

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Work and Energy

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  1. Work and Energy Work = Force X distance W = Fd • Unit - Joules (N m), (kg m2/s2) • Force must be in the direction of the motion.

  2. Work and Direction Lifting a box is work • Fighting force of gravity. • Lifting force in same direction box moves. Your lifting force and the boxes direction Fighting against the force of gravity

  3. Work and Direction Pushing a box is work • Applied force is in the direction of movement • Working against force of friction • Pushing on ice would be less work Frictional Force

  4. Work and Direction Carrying a box is not work Your lifting force But this is the direction of motion Fighting against the force of gravity

  5. Work and Direction Mowing the lawn is some work • only do work in horizontal direction. • The downward push, because of the angle of the handle, doesn’t do any work. Your push This is the only part that does work This part is lost

  6. Vertical vs. Horizontal Work Lifting Gives an object Potential Energy of position. Pushing Gives an object Kinetic Energy of Motion.

  7. Work or Not • A teacher pushes against a wall until he is exhausted. • A book falls off the table and falls freely to the ground. • A waiter carried a full try of meals across the room. • A rocket accelerates through space. • A rocket travels at a constant speed through space

  8. Work: Example 1 How much work is done lifting a 5.0 kg backpack to a shelf 2.0 meters above the floor?

  9. Superman does 36,750 J of work lifting this car 2.5m from the ground? What is the weight of the car? What is the mass of the car?

  10. Work: Example 2 Mr. Fredericks pulls a box with 30 N of Force a distance of 5.0 m, at an angle of 50o with the ground. How much work was done? Direction of motion q = 50o

  11. Fx = (30N)(cos50o) = 19 N Fy = (30N)(sin50o) = 23 N W = Fxd = (19N)(5m) = 96J W = Fdcosq Fy q = 50o Fx

  12. A sled is pulled with a force of 100.0 N at an angle of 65o to the ground for 8.00 m. Calculate the work done. (338 J)

  13. Work: Example 3 A 50-kg crate is pulled 40 m with a force of 100 N at an angle of 37o. The floor is rough and exerts a frictional force of 50 N. Determine the work done on the crate by each force and the net work done on the crate. Fp q Ffr FN mg

  14. Let’s deal with the vertical forces first WG = mgxcos90o = 0 WN = FNxcos90o = 0 No work is done in the vertical direction (the box is not lifted)

  15. Now the horizontal forces Wfr = Ffrd Wfr = (50 N)(40m) = -2000 J Wp = Fpdcos 37o Wp = (100N)(40 m)(cos 37o) = 3200 J Wnet = WG + Wfr Wnet = 0 + 0 + 3200 J -2000 J = 1200 J

  16. Example 4 A hiker walks up a hill at a constant speed. He is carrying a 15.0 kg backpack and the hill is 10.0 m high. How much work did he do? Surprisingly, he does no work in the horizontal direction.

  17. The only forces are vertical SF = FH-mg ma = FH-mg (no acceleration) 0 =FH-mg FH = mg = (15.0 kg)(9.80 m/s2) FH = 147 N Whiker = Fd = (147 N)(10.0 m) Whiker = 1470 J

  18. How much work did gravity do? WG = -1470 J WNET = Whiker + WG WNET = 1470 J -1470 J = 0

  19. Does the Earth Do Work on the Moon? W = Fdcosq W = Fd(cos 90o) W = Fd(0) W = 0 v FR

  20. English Unit of Work • Foot-pound – English unit of work. • Pound – unit of Force • W = Fd = (foot*pound)

  21. Variable Force Work is really an area: W =∫Fdx (an integral tells you the area) WORK

  22. Given the following graph, determine the work done by the following force in the first ten meters Distance (m)

  23. Calculate the work: • In the first 10 meters • In the second 10 meters • Overall Distance (m)

  24. Calculate the work: • In the first 20 meters • From 20 to 40 meters • From 40 to 80 meters d) Overall

  25. Calculate the work: • In the first 10 meters • In the second 10 meters • Overall

  26. Calculate the work: • In the first 10 meters • In the second 10 meters • Overall Distance (m)

  27. A 35.0 kg suitcase is pulled 20.0 m with a force of 100.0 N at an angle of 45.0o. The floor is has a mk of 0.200. • Calculate the normal force on the suitcase (HINT: take the Fpy into account). (272 N) • Calculate the work done by friction. (-1088 J) • Calculate the work done by the pull. (1414 J) • Calculate the net work on the suitcase. (326 J) Fp q Ffr FN mg

  28. A 50.0 kg child and sled is pulled by a rope with a tension of 200.0 N and an angle of 35.0o with the ground for 50.0 m. The sled and snow has a mk of 0.150. • Calculate the normal force on the sled. (375 N) • Calculate the work done by friction. (- 2813 J) • Calculate the work done by the pull. (8191 J) • Calculate the net work on the sled. (5379 J)

  29. Energy Energy – The capacity to do work • 1 Joule = 1 Newton-meter =1 kg-m2/s2 • Two types • Potential Energy • Kinetic Energy

  30. Kinetic Energy • Definition - Energy of motion • K = ½ mv2 • m = mass (kg) • v = speed (m/s) • Unit = Joules Questions: • If the mass of an object is doubled, what happens to KE? • If the speed is doubled, what happens to KE?

  31. A kitten is traveling with a kinetic energy of 10.0 J at 2.00 m/s • Calculate his mass • If Mr. Fredericks (56.0 kg) has the same kinetic energy, calculate his speed.

  32. Kinetic Energy If Mr. Fredericks (56 kg), had the same kinetic energy as the Thing in the previous example, how fast would he move?

  33. Kinetic Energy and Work WNET = KEf – KEI WNET = DKE

  34. How much work is required to accelerate a 1000-kg car from 20-m/s to 30-m/s? (W = 250,000 J)

  35. A 1000 kg car stops over 50.0 m. The coefficient of friction is 0.25. • Calculate the force of friction. (-2450 N) • Calculate the work done by friction. (-1.225 X 105 J) c) Calculate the initial speed of the car. (15.7 m/s)

  36. A 400.0 g football travelling at 25.0 m/s is caught by a player. The players arms go back 75.0 cm while catching the ball. • Calculate the initial kinetic energy of the ball. (125 J) • Calculate the force the ball exerted on the player’s hand. (167 N)

  37. A 140.0 g baseball is caught by a fielder. The glove moves 25.0 cm. The fielder experienced and average force of 204 N. • Calculate the kinetic energy of the ball before being caught. (51 J) • Calculate the initial speed of the ball. (27.0 m/s) • Draw a free body diagram of the ball in the air. • Draw a free body diagram of the ball while being caught by the glove.

  38. Potential Energy • Definition - Stored energy • Two Types • Energy of position • Gravitational PE - stored by placing something at a height above the ground • Mechanical PE - compressing a spring or mechanical device • Energy stored in chemical bonds and atomic nuclei

  39. Potential Energy of Position PE = mgy m = mass in kg g = acceleration of gravity (9.8 m/s2) y = height from the ground in meters.

  40. Potential Energy of Position . What would the potential energy of a ball be at the other steps? 45 J 15 J

  41. Potential Energy and Work W = DPE W = mgy

  42. How much work does a 50.0 kg woman do by climbing to the top of a 300 m hill?

  43. Assume the roller coaster car has a mass of 1000 kg. Calculate the PE: • At pts. A, B, and C • Gained from A B • Lost B  A • Lost B  C

  44. Hooke’s Law Fx = kx F = Force exerted on the spring k = spring constant x = distance compressed or stretched.

  45. A force of 600 Newtons will compress a spring 0.5 meters. • Calculate the spring constant of the spring. (1200 N/m) • Calculate the force is necessary to stretch the spring by 2 meters. (2400 N) • A force of 40 Newtons will stretch a different spring 0.1 meter. How far will a force of 80 Newtons stretch it? (0.2 m)

  46. Springs PE = ½ kx2 k = spring constant (measure of the stiffness of a spring) x = distance stretched from normal length

  47. Spring Example 1 How much potential energy is stored in a spring if it is compressed 10.0 cm from its normal length. Assume it has a spring constant of 300 N/m PE = ½ kx2 PE = ½ (300 N/m)(0.100 m)2 PE = 1.5 N-m = 1.5 J

  48. When 10 J is used to stretch a spring, the spring stretchs 20.0 cm. Calculate the spring constant.

  49. Conservative and Nonconservative Forces Conservative Forces • Work is independent of the path taken • Gravity, elastic spring Nonconservative Forces • Work depends on the path taken • Friction, air resistance, tension in a cord • Also called dissipative forces

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