Chapter 6 Work And Energy

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Chapter 6 Work And Energy

  1. 1. Work, Energy and Power
  2. 2. WORK Work is done whenever a force (F) is exerted and whenever there is displacement (s). (s). The amount of work done is proportional to both the force and displacement. (W = F x s) Work is measured in newton-meters. newton- 1 joule of work = 1 newton of force x 1 meter of distance James Prescott Joule
  3. 3. Units of Work
  4. 4. Force and displacement do not point in the same direction W = (F cos θ )s the product of the component of force (F) in the direction of the displacement (s) and the magnitude of the displacement cos 0 = 1 o produced by that force cos 90 = 0 o W= ( F cos θ ) s θ = angle between the direction of F and cos180 = −1 o that of S
  5. 5. Work Done by a Constant Force Example: Pulling a Suitcase-on-Wheels Find the work done if the force is 45.0-N, the angle is 50.0 degrees, and the displacement is 75.0 m. [ ] W = (F cos θ )s = (45.0 N ) cos 50.0o (75.0 m ) = 2170 J
  6. 6. Work Done by a Constant Force a. The weight lifter is bench pressing a barbell whose weight is 710 N. b. He raises the barbell at a distance of 0.65 m W = (F cos 0)s = Fs c. He lowers the barbell at the same distance W = (F cos180)s = − Fs
  7. 7. WORK
  8. 8. Working against Gravity W = F x s; if F = mass x gravity (9.8 m/s2) Then: W = (mg) x d Wgravity = mg (hf – hi) (h How much work against gravity would a 50-kg person 50- do if he climbs a flight of stairs 3 meters high?
  9. 9. Energy Ability to do work No energy, no work property of a body or system of bodies by which work can be done or performed The energy possessed by a body is equal to the total work it can do (W = E) Both are scalar quantity; same unit (joules) Types – Kinetic Energy: energy associated with moving objects – Gravitational potential energy: form of energy waiting to be released
  10. 10. Energy
  11. 11. Energy 1019 Joules 1027 Joules
  12. 12. Kinetic Energy Two factors governing an object’s kinetic energy: energy: – Kinetic energy is proportional to the mass – Kinetic energy increases as the square of its velocity Kinetic energy equals the mass of the moving object times the square of that object’s velocity, multiplied by the constant ½. Kinetic energy (joules) = ½ X mass (kg) x [Velocity (in m/s)]2 KE = ½ mv2
  13. 13. Kinetic Energy (KE) The KE of an object of mass m and speed v If E = W; and W = F x s; then F X s = ( ma) X (1/2 at2) = 1/2 m X ( at) 2 since v = at therefore KE = 1/2 m v 2
  14. 14. Sample Problem Find the KE of a body with a mass of 10 kg and a speed of 10 m/s 500 joules How much energy is required to accelerate a 1000-kg car from rest to 1000- 30 m/sec, assuming no friction. friction. 4.5 x 105 joules
  15. 15. Potential energy Potential energy is the energy that could result in the exertion of a force over a distance. distance. Energy on account of their position Stored energy Most common = gravitational PE
  16. 16. Gravitational Potential Energy The gravitational potential energy PE is the energy that an object of mass (m) has by virtue of its position relative to the surface of the earth. The gravitational potential energy of an object equals its weight (the force of gravity exerted on the object) times its height above the ground (the object has been lifted above the surface of the earth). Potential Energy (joules) = mass (kg) x g (m/s2) x height (m) PE = mgh
  17. 17. Sample Problem Find the GPE of an object with a mass of 100 kg raised to 2m above ground? 1960 J A 12-kg suitcase is lifted 0.75 12- m above the ground. 88.2 J
  18. 18. Work and Conservative Force Version 1 A force is conservative when the work it does on a moving object is independent of the path between the object’s initial and final positions. Version 2 A force is conservative when it does no work on an object moving around a closed path, starting and finishing at the same point. The track exerts a normal force but the force is directed perpendicular to the motion ,hence, no work is done
  19. 19. Work and Non - Conservative Force A force is nonconservative if the work it does on an object depends on the path of the motion between the points An example of a nonconservative force is the kinetic frictional force. When an object slides over a surface, the kinetic frictional force points opposite to the sliding motion and does negative work W = (F cos θ )s = f k cos 180 o s = − f k s
  20. 20. Conservative and Nonconservative Forces WORK – ENERGY THEOREM In normal situations both conservative and nonconservative forces act simultaneously on an object, so the work done by the net external force can be written as W = Wc + Wnc W = KE f − KE o = ∆KE Wc = Wgravity = mgho − mgh f = PE o − PE f = −∆PE
  21. 21. Conservative Versus Nonconservative Forces W = Wc + Wnc ∆KE = − ∆PE + Wnc THE WORK-ENERGY THEOREM Wnc = ∆KE + ∆PE Wnc = Ef + Eo Ef = Eo
  22. 22. Conservation of Energy If there are no forces doing work on a system (conserved), the total mechanical energy (E) of the conserved), (E) system (sum of the KE and PE) remains constant E = KE + PE = constant Principle of Conservation of Energy E before = E after Energy can neither be created not destroyed, but can only be converted from one form to another.
  23. 23. Conservation of Energy As demonstrated by a pendulum E = PE = mgh E = PE = mgh E = KE = ½ mv2
  24. 24. Conservation of Energy: Energy of a Falling Body At the beginning of a fall just before an object is released, its energy is all potential. As the object falls, potential energy is gradually converted to kinetic energy The kinetic energy at the end of a fall is equal to the potential energy at the beginning. Initial PE = Final KE mgh = ½mv2 gh = ½v2 or v = √2gh
  25. 25. Food and Energy Food: type of chemically stored energy The energy content of food is in kilocalories 1 kilocalorie = 4186 joules
  26. 26. Food and Energy FOOD kcal/g ACTIVITY ENERGY CONSUMPTION RATE (kcal/min) Apples 0.58 Sleeping 1.2 Avocado 1.67 Sitting in class 3.0 Beer 0.42 Walking slowly 3.8 Big Mac 2.89 Cycling 5.7 Butter 7.20 Playing tennis 6.3 Swimming 6.8 Chocolate 5.28 Climbing stairs 9.8 Eggs 1.63 Playing basketball 11.4 Sugar 4.00
  27. 27. Power The rate at which work is done. The rate at which done. energy is expended. expended. Power is the amount of work done divided by the time it takes to do it. it. Power is the energy expended divided by the time it takes to expend it. it. Power (watts) = Work (joules) Power (watts) = Energy (joules) Time (sec) Time (sec) James Watt ; 1 horsepower = 550 ft-lb of work/second = 746 watts or 0.746 kilowatt
  28. 28. Sample Problem Calculate the amount of power generated by a 60-kg person climbing a 2 m high flight of 60- stairs in 7 sec. sec. P = W /t ; since W = mgh ,Then P = mgh t = (60 kg) ( 9.8 m/s2) ( 2 m ) 7s = 1176 J 7s = 168 W
  29. 29. Sample Problem If the cost per kilowatt hour is 50 cents, what is the cost of running a 500-watt 500- color TV set at 6 hours per day for 30 days? P 45.00
  30. 30. Power
  31. 31. The rate of conversion of food energy to some other form is called metabolic rate. The total energy conversion rate of a person at rest is called basal metabolic rate BMR of an individual is related to thyroid activity The BMR is directly related to the mass of the person. Energy consumption is directly proportional to oxygen consumption

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