Chapter 9 Work

1. Chapter 9 Work Conceptual Physics Chapter 9

2. Work Defined • In physics, when work is done • There must be a force applied to an object. • The object must undergo a displacement as a result of the applied force. • The force and the displacement must share a common direction. Work = Force x Displacement W = FΔx Conceptual Physics Chapter 9

3. Work Defined • Work is a scalar quantity. • Work can have a positive value (when the force and displacement are parallel) or a negative value (when force and displacement are anti-parallel). • Work is measured in Joules (1 J = 1 N·m) Conceptual Physics Chapter 9

4. Work Defined • Work will generally fall into one of two categories: • Work done in opposition of another force (e.g., push a crate across the floor against the force of friction) • Work done to change the speed of an object (e.g., a braking force brings a truck to a stop) Conceptual Physics Chapter 9

5. Positive Work If the power lifter raises 125 kg from the floor to a position 2 m above the floor with a constant velocity, how much work does he do on the weight? W = FΔx W = mgh W = 125 kg(10 m/s2)(2 m) W = 2500 J I must apply an upward force equal to the weight of the bar The work done is positive since the force and the displacement are in the same direction. Conceptual Physics Chapter 9

6. Zero Work How much work is done if the athlete holds the 125 kg bar above his head (still 2 m above the floor)? I’m exerting a force, but I’m not doing any work! Conceptual Physics Chapter 9

7. Negative Work How much work is done by the athlete if he lowers the bar to the floor with a constant velocity? W = FΔx W = mgh W = 125 kg(10 m/s2)(-2 m) W = -2500 J I still must apply an upward force equal to the weight of the bar The work done is negative since the force and the displacement are in the opposite direction. Conceptual Physics Chapter 9

8. More Work If the woman slides the crate across the floor a distance, d, by applying a force, F, at an angle, θ, above the horizontal, how much work does she do on the crate? We are only interested in the component of the force that acts along the direction of motion W = FΔx W = F‼d Conceptual Physics Chapter 9

9. Work As long as he does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion. How much work does the man do on the bag of groceries? Conceptual Physics Chapter 9

10. W Work P = Power = t Time Power • Power is the rate at which work is done. • Power is a scalar quantity. • Power is sometimes measured in horsepower; the SI unit for power is the Watt (1 W = 1 J/s) or Conceptual Physics Chapter 9

11. Question A student is asked to walk at a leisurely pace up a flight of stairs and then sprint up the same flight of stairs. In which case does the student do more work? In which case does the student generate more power? Conceptual Physics Chapter 9

12. Energy • Energy can be defined as the ability to do work. • Energy can take many forms. • Energy is a scalar quantity and is measured in Joules. • Mechanical energy can be classified as either potential energy or kinetic energy. Conceptual Physics Chapter 9

13. Potential Energy • Potential energy is energy that is stored in a body due to its position. • Springs and rubber bands store energy in the form of elastic potential energy (EPE). • The energy due to the position of an object in a gravitational field is called gravitational potential energy (GPE). Conceptual Physics Chapter 9

14. Potential Energy The amount of gravitational potential energy possessed by an elevated object is equal to the work done against gravity to raise the object. GPE = W = FΔx = mgh Conceptual Physics Chapter 9

15. Potential Energy GPE = mgh • h is the height above an arbitrarily chosen reference level. • Since the gravitational potential energy is dependant on the reference level, it is impossible to state an absolute value for the GPE of a body – we can only state GPE values relative to the reference level. • Changes in potential energy are not dependant on the chosen reference level. Conceptual Physics Chapter 9

16. Kinetic Energy • Kinetic energy is the energy an object has due to its motion. • Kinetic energy depends on the mass of the object and the speed of the object. • Notice that kinetic energy is dependant on the square of the velocity, so if the velocity is doubled the kinetic energy is quadrupled. Kinetic Energy = ½ mass x velocity2 KE = ½mv2 Conceptual Physics Chapter 9

17. Kinetic Energy • The change in kinetic energy of a body is equal to the work done on the body. • When positive work is done, kinetic energy increases. Negative work causes a decrease in kinetic energy. W = ΔKE F·Δx = ½mvf2 - ½mvi2 This is called the work-energy theorem. Conceptual Physics Chapter 9

18. Conservation of Energy • Energy can be transferred from one object to another (e.g., energy is transferred from a moving vehicle to a stationary vehicle when they collide). • Energy can be transformed from one type to another (e.g., elastic potential energy of a stretched bowstring is converted to kinetic energy of an arrow fired from it). • The total amount of energy in the universe remains constant! Conceptual Physics Chapter 9

19. Conservation of Energy GPE = 22500 J The Amazing Talia jumps from a platform 45 m high into a small bucket of water below. Talia’s mass is 50 kg. How much potential energy does she have initially? GPE = mgh = 50 kg(10 m/s2)(45 m) = 22500 J Conceptual Physics Chapter 9

20. Conservation of Energy GPE = 22500 J KE = 0 J The Amazing Talia jumps from a platform 45 m high into a small bucket of water below. Talia’s mass is 50 kg. How much kinetic energy does she have initially? KE = ½mv2 since she is not moving, KE is zero. Conceptual Physics Chapter 9

21. Conservation of Energy GPE = 22500 J KE = 0 J The Amazing Talia jumps from a platform 45 m high into a small bucket of water below. Talia’s mass is 50 kg. GPE = 15000 J KE = 7500 J If we know that at position 1 Talia has 15000 J of potential energy, how much kinetic energy does she have? GPE + KE = 22500 J KE = 22500 J – 15000 J Total energy must be conserved. KE = 7500 J Conceptual Physics Chapter 9

22. Conservation of Energy GPE = 22500 J KE = 0 J The Amazing Talia jumps from a platform 45 m high into a small bucket of water below. Talia’s mass is 50 kg. GPE = 15000 J KE = 7500 J GPE = 11250 J KE = 11250 J Since she is only half as high as her starting position, she has only half as much potential energy as she started with. How much potential energy does she have when she has fallen half-way to the bucket? The remaining potential energy has been converted to kinetic energy. Conceptual Physics Chapter 9

23. Conservation of Energy GPE = 22500 J KE = 0 J The Amazing Talia jumps from a platform 45 m high into a small bucket of water below. Talia’s mass is 50 kg. GPE = 15000 J KE = 7500 J GPE = 11250 J KE = 11250 J How much potential energy does she have when she reaches the bucket? Since h is zero, she has no potential energy relative to the bucket. GPE = 0 J Conceptual Physics Chapter 9

24. Conservation of Energy GPE = 22500 J KE = 0 J The Amazing Talia jumps from a platform 45 m high into a small bucket of water below. Talia’s mass is 50 kg. GPE = 15000 J KE = 7500 J GPE = 11250 J KE = 11250 J Total energy is conserved – all of the potential energy she had initially has now been transformed to kinetic energy. How much kinetic energy does she have when she reaches the bucket? GPE = 0 J KE = 22500 J Conceptual Physics Chapter 9

25. Conservation of Energy GPE = 22500 J KE = 0 J The Amazing Talia jumps from a platform 45 m high into a small bucket of water below. Talia’s mass is 50 kg. GPE = 15000 J KE = 7500 J GPE = 11250 J KE = 11250 J KE = ½mv2 What is her velocity when she reaches the bucket? 22500 J = ½(50 kg)v2 v2 = 900 J/kg v = 30 m/s GPE = 0 J KE = 22500 J Conceptual Physics Chapter 9

26. Simple Machines • Machines can change the magnitude of a force (increase or decrease) or the direction of the force. • In an ideal machine (no friction), the work output will be equal to the work input. • In any real machine, the output work will be less than the input work due to friction and other inefficiencies. Conceptual Physics Chapter 9

27. Simple Machines • There are six different categories of simple machines: Conceptual Physics Chapter 9

28. The Lever First-class lever This means we can lift the load by applying a downward force that is less than the weight! If we call the applied force Fin and the load Fout, we can say that Fin is less than Fout since the fulcrum is closer to the load. The input force (or effort) is where we apply a force. The output force (or load or resistance) is where the desired work is accomplished. Fin Fout Fout The position of the fulcrum will determine the mechanical advantage of the lever. The pivot point is called the fulcrum Conceptual Physics Chapter 9

29. The Lever First-class lever Although the input force gets increased, the output work must be no larger than the input work. Wout = Win Fin·din = Fout·dout Fin Fout Conceptual Physics Chapter 9

30. The Lever 200 N First-class lever The actual mechanical advantage (AMA) of the lever is found from the ratio of output force to input force. If a 100 N effort is required to raise a 200 N load, we can find the actual mechanical advantage. AMA = = = 2 100 N Fin Fout Conceptual Physics Chapter 9

31. The Lever • There are three classes of levers: The mechanical advantage can be less than, greater than, or equal to one depending on the position of the fulcrum. A first class lever has the fulcrum placed between the load and the effort. (e.g., a playground see-saw) The mechanical advantage will always be greater than one. A second class lever has the load placed between the fulcrum and the effort. (e.g., a wheelbarrow) The mechanical advantage will always be less than one. A third class lever has the effort placed between the fulcrum and the load. (e.g., a broom) Conceptual Physics Chapter 9

32. 6 m = 3 m The Inclined Plane The height of an inclined plane is the output distance (dout), the length of the inclined plane is the input distance (din). The ideal mechanical advantage can be found from a ratio of these distances. din IMA = = 2 dout Conceptual Physics Chapter 9

33. The Wedge • A wedge is simply two inclined planes positioned back-to-back. • The mechanical advantage of a wedge is controlled by the slope. • The ideal mechanical advantage is the ratio of the slope over the thickness. • All cutting tools are a form of a wedge. Conceptual Physics Chapter 9

34. The Screw • A screw is an inclined plane wrapped around a cylinder. • The mechanical advantage is controlled by the pitch – the distance between adjacent threads on the screw. Conceptual Physics Chapter 9

35. The Pulley A moveable pulley has an ideal mechanical advantage of two and does not change the direction of the force. A single fixed pulley has an ideal mechanical advantage of one and changes the direction of the force. A block and tackle is a compound pulley system that has an ideal mechanical advantage of greater than one. Conceptual Physics Chapter 9

36. The Wheel and Axle • A large diameter wheel is rigidly fixed to a smaller diameter axle. • The ideal mechanical advantage is controlled by a ratio of these diameters. Conceptual Physics Chapter 9

37. Wout Fout dout Win Fin din AMA IMA Efficiency • The efficiency of any simple machine can be found from a ratio of the work output to the work input. Efficiency = X 100 (stated as a percentage) this ratio is the reciprocal of the ideal mechanical advantage this ratio is the actual mechanical advantage = Conceptual Physics Chapter 9

38. Energy Sources • The sun is the source of practically all our energy on Earth. • Sunlight is directly transformed into electricity by photovoltaic cells. • We use the energy in sunlight to generate electricity indirectly as well: • evaporation • precipitation • rainwater flows into rivers • hydroelectric power Conceptual Physics Chapter 9

39. Energy Sources • Wind, caused by unequal warming of Earth’s surface, is another form of solar power. • The energy of wind can be used to turn generator turbines within specially equipped windmills. Conceptual Physics Chapter 9

40. Energy Sources • Hydrogen is the least polluting of all fuels. • Because it takes energy to make hydrogen—to extract it from water and carbon compounds—it is not a source of energy. Conceptual Physics Chapter 9

41. Energy Sources • An electric current can break water down into hydrogen and oxygen, a process called electrolysis. • If you make the electrolysis process run backward, you have a fuel cell. • In a fuel cell, hydrogen and oxygen gas are compressed at electrodes to produce water and electric current. Conceptual Physics Chapter 9

42. Energy Sources • The most concentrated form of usable energy is stored in uranium and plutonium, which are nuclear fuels. • Earth’s interior is kept hot by producing a form of nuclear power, radioactivity, which has been with us since the Earth was formed. Conceptual Physics Chapter 9

43. Energy Sources • A byproduct of radioactivity in Earth’s interior is geothermal energy. • Geothermal energy is held in underground reservoirs of hot water. • In these places, heated water near Earth’s surface is tapped to provide steam for running turbogenerators. Conceptual Physics Chapter 9

44. The Pulley Conceptual Physics Chapter 9