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South Pasadena Physics Name____________________ Period___ 8 Work and Energy Practice Test 1Work The SI unit for work is the joule (J), which equals one Newton-meter (N-m). For maximum work to be done, the object must move in the direction of the force. If the object is moving at an angle to the force, determine the component of the force in the direction of motion, using 3. After finishing her physics homework, Sarah pulls her 50.0 kg body out of the living room chair and climbs up the 5.0 m high flight of stairs to her bedroom. How much work does Sarah do in ascending the stairs? (Hint: The number of stairs or the slope of the stairs is irrelevant. All that is important is the change in position.) W = F x displacement cos θ Remember, if the object does not move, or moves perpendicular to the direction of the force, no work has been done. Problems: 1. Bud, a very large man of mass 130 kg, stands on a pogo stick. How much work is done as Bud compresses the spring of the pogo stick 0.050 m? 2. The SI unit for power is the watt (W), which equals one joule per second (J/s). One person is more powerful than another if he or she can do more work in a given amount of time, or can do the same amount of work in less time. Fill in the missing information: Work (J) 2 Power Power is the rate at which work is done. Power = work Elapsed time Force (N) Distance (m) a) 45.0 ? 2.0 b) 122 3.0 ? c) ? 28.0 30.0 cm d) ? 75.0 kg firefighter climbs a flight of stairs. 10.0 m high Problems: 4. In the problem in station 1 where Sarah (50.0 kg) climbed the 5.0 meter high staircase, she took 10.0 seconds to go from the bottom to the top. The next evening, in a rush to catch her favorite TV show, she runs up the stairs in 3.0 seconds. a) What values of power does she generate each night? b) On which night does Sarah do more work? c) On which night does Sarah generate more power? 3 5. Fill in the missing information: Power (Watts) Work (Joules) Time (seconds) Potential Energy Energy is the ability to do work. The two kinds of energy we are dealing with in this chapter are the energy of position or stored energy (potential energy) and the energy of motion (kinetic energy). Gravitational potential energy relies upon the vertical change in height and not upon the path taken. a) 60.0 20.0 ? b) 240 ? 2.5 c) ? 183 5.5 d) 3.5kilowatts 4.8 x 10-3 ? Potential Energy = m g h 2.0 megajoules 25.0 Other forms of stored energy exist, such as when a bow is pulled back and before it is released, the energy in the bow is equal to the work done to deform it. This stored or potential energy is written as Δ PE = F Δd The unit of potential energy (like work) is Joules. e) ? Problems: 6. Which requires more power: Lifting a 2.0 kg object to a height of 2.0 m in a time of 2.0 seconds or lifting a 4.0 kg object to a height of 1.0 meter in a time of 3.0 seconds? (Hint: mass in kg is not a force) 7. Atlas and Hercules, two carnival sideshow strong men, each lift 200.0-kg barbells 2.00 m off the ground. Atlas lifts his barbells in 1.00 s and Hercules lifts his in 3.00 s. a) Which strong man does more work? b) Calculate which man is more powerful. 8. Legend has it that Isaac Newton “discovered” gravity when an apple fell from a tree and hit him on the head. If a 0.20 kg apple fell 7.0 m before hitting Newton, what was its change in PE during the fall? 9. It is said that Galileo dropped objects off the Leaning Tower of Pisa to determine whether heavy or light objects fall faster. If Galileo had dropped a 5.0 kg cannon ball to the ground from a height of 12 m, what was the change in PE of the cannon ball? Fill in the missing information: 10. Potential Energy (J) Mass (kg) Height (m) a) 50.0 75.0 ? b) 280 ? 1.8 c) ? 17.3 5.5 d) 3.5 kilojoules 4.8 x 10-3 ? 14. A car with 54,000 joules of kinetic energy is moving at 35 m/s? What is the car’s mass? 15. An oxygen molecule of mass 5.31 x 10-26 kg, has a kinetic energy of 6.21 x 10-21 Joules. How fast is it moving? 16. If the kinetic energy of an arrow is doubled, by what factor has its velocity increased? 4 Kinetic Energy KE = ½ mv2 Kinetic Energy is the energy of motion and varies with the square of the speed. Kinetic Energy = ½ mass x (velocity)2 and the SI unit of KE is also Joules, which is the same unit used for work. When work is done on an object, energy is transformed from one form to another. The sum of the changes in potential, kinetic and heat energy is equal to the work done on the object. 17. If the velocity of the arrow is doubled, by what factor does its kinetic energy increase? 5 11. A greyhound at a race track, can run at a speed of 16.0 m/s. What is the K.E. of a 20.0 kg greyhound as it crosses the finish line? 12. A 7.0 kg bowling ball is moving at 2.0 m/s. What is it’s Kinetic Energy Conservation Energy of According to the law of conservation of energy, energy cannot be created or destroyed, but remains constant in a system, when no forces are acting other than gravity. Δ KE = ΔPE or Total Mechanical Energy = P.E. + K.E. KE I + PE I = KE f + PE f 13. An 1800 kg truck has a kinetic energy of 95,000 Joules. What is the truck’s velocity? For a bowling ball, the equation simplifies to mgh = ½ mv2, so then Velocity at bottom = √2gh 6 Problems: Work-Energy Theorem Work done on an object = change in its K.E. F x d = change in Kinetic Energy 18. A 7.5 kg bowling ball is brought back to a height of 1.2 meters and released. How much kinetic energy will it have at the lowest point in its swing? 19. What will be the velocity of the bowling ball above at the lowest point? 20. When the bowling ball above is released, how much kinetic energy will it have when it is 0.60 meters above its lowest point? 21. How much kinetic energy will the bowling ball have when it swings to the highest point on the other side of its swing? 22. How much potential energy will the bowling ball have when it swings to the highest point on the other side of its swing? 24. How much work must be done to stop a 1000 kg car traveling at 31 m/s? 25. When the brakes of a motorcycle traveling at 60 km/hr become locked, how much farther will the motorcycle skid than if it were traveling at 20 km/hr? 26. How much work is required to stop an electron (m= 9.11 x 10-31 kg), which is moving with a speed of 1.90 x 106 m/s? 27. A car does 7.0 x 104 J of work in traveling 2.8 km (2,800 m) at constant speed. What was the average retarding force (from all sources) acting on the car? 7 Efficiency Efficiency is the ratio of the work output to the work input and has no units and is usually expressed as a percentage. 23. If you turn on the radio in your car with the engine off, will more gasoline be burned later when the car engine is turned on, as a result of having turned on the radio? a) YES b) NO Efficiency = work output x 100 work input or AMA x 100 IMA 28. A bicycle rider is doing 35 joules of work for a return of 32 joules of work output by the bicycle. What is the efficiency of the bicycle? 8Machines Machines are devices that help do work by changing the magnitude or direction of the applied force. 32. What is the mechanical advantage of this machine? 33. A crate of bananas weighing 3000 N is shipped from South America to New York, where it is unloaded by a dockworker, who lifts the crate by pulling on the rope of a pulley system with a force of 200 N. What is the actual mechanical advantage of the pulley system? Work In = Work Out or Fxd = Fxd Examples of machines include: A lever A pulley An inclined plane 34. If the worker above lifted the crate of bananas a distance of 10 m, what distance of rope did he pull? FORMULAS for MACHINES Work in = Work out Actual Mechanical Advantage = F out/F in or Ideal Mechanical Advantage = distance in / distance out 29. If a force of 25 Newton is applied in order to lift a 45 Newton weight a distance of 125 cm, then what distance must the applied force be moved, using a lever? 9 Miscellaneous 35. If the dials on an electric meter read 23810 for the initial reading and then read 23890 for the final reading 3 days later, what is the cost for the energy if the Edison company charges $.15 per kilowatt - hour? 30. What is the mechanical advantage of this machine? 31. A lever is used to lift a 25 kilogram lead mass a distance of 40 cm. If the distance that the input force is moved is 80 cm, what is the amount of force used to lift the mass? 36. If you leave on a 100 watt light bulb in a lamp for a time period of 10 hours, how many kilowatt - hours of energy is being consumed? 37. How much will it cost to operate that 100 watt bulb for the 10 hours? 38. Which is more costly? Operating a 60 watt bulb for 5.0 hours or operating a 100 watt bulb for a time period of 2.5 hours? (Hint: Calculate the kilowatt-hours for each bulb and then multiply by $.15 per kilowatt – hour) 39. Is a hand-held generator easier or harder to crank when a light bulb is screwed into it? a) easier b) harder Consider the lab done in class called “Making the Grade” where a cart was pulled up a ramp of varying angles. 42. Considering that varying angles were used for the placement of the wooden board, was cosine used in the calculation of the work done? Explain why or why not? ___________________________________ ___________________________________ ___________________________________ ___________________________________ 43. Would you expect the calculated work to be approximately the same or to be different for two different trials of a 25 angle of incline and a 45 angle of incline? Explain why or why not? ___________________________________ ___________________________________ ___________________________________ ___________________________________ 40. Is a hand-held generator easier or harder to crank when the light bulb is screwed into it but it is burned out? a) easier b) harder 41. If two identical cars are speeding along and then they both apply their brakes, for the car traveling at twice the speed, how much more distance will be required to come to a stop, compared to the car that is traveling at half the speed? 44. In a laboratory experiment, a student tries to duplicate the demonstration shown in class, using the bowling ball pendulum. If the distance that the bowling ball is brought back is 13.5 cm above its lowest point, then what speed would you expect it to have at its lowest point after being released? a) both cars require the same braking distance b) faster car will require twice the braking distance c) faster car will require four times the braking distance. d) faster care will require nine times the braking distance. _____________________________ floor ANSWERS to Chapter 8 Practice Test (Work and Energy) 6. Lifting 2.0 kg mass (20 Watts): (Other mass requires 13 W) 1. Weight = 130 kg x 9.8 m/s2 = 1274 N Work = 1274 N x 0.050 m = 63.7 or 64 J 7. a) Both do the same amount of work b) Atlas is more powerful (4,000 Watts) 2. 8. 0.20 kg x 9.8 m/s2x 7.0 m =13.7 J Work (J) Force (N) Distance (m) 45.0 22.5 N 2.0 122 3.00 40.7 m 10. 28.0 30.0 cm Potential Energy (J) Mass (kg) Height (m) 75.0 kg firefighter climbs a flight of stairs 10.0 m high 50.0 75.0 0.0680 m 280 15.9 kg 1.80 932 J 17.3 5.50 3.5 kilojoules 4.8 x 10-3 74,405 m 8.40 J 7,350 J 2 3. Weight = 50.0 kg x 9.8 m/s = 490 N Work = 490 N x 5.0 m = 2,450 J 4. a) Sarah does the same work both nights nd 9. 5.0 kg x 9.8 m/s2x 12 m =588 J 11. KE = ½ x 20.0 kg x (16.0 m/s)2 = 2,560 J 12. KE = ½ x 7.0 kg x (2.0 m/s)2 = 14 J b) More power generated 2 night c) 1st night = 250 W; 2nd night = 817 W 13. v = (2 x 95,000 J/1800 kg)1/2 = 10.3 m/s 14. mass = (2 x 54,000 J)/ (35 m/s)2 = 88 kg 5. Power (Watts) Work (Joules) Time (seconds) 60.0 20.0 .33 s 240 600 J 2.5 33 W 183 5.5 -3 3.5 kilowatts 4.8 x 10 80,000 W 2.0 megajoules 15. v = (2 x 6.21 x 10-21 J/5.31 x 10 –26 kg)1/2 = 484 m/s → 2 KE = ½ mv2 v = √2 =1.41 1.41 x greater 16. KE = ½ mv2 17. KE = ½ mv2 → KE = ½ m2v2 2v2 = 4x greater 1.4 x 10-6 25.0 18. PE I = KE f = 7.5 kg x 9.8 m/s2 x 1.2 m = 88 J 19. v = √(2gh) = √(2 (9.8 m/s2) 1.2 m) = 4.849 or 4.8 m/s 33. A.M.A. = 3,000 N/200 N = 15 34. d = (3,000 N x 10 m) / 200 N =150 m 20. (K.E. – mgh) = 88 J – (7.5 kg x 9.8 m/s2 x 0.6 m) = 88 J – 44 J = 44 J 35. 80 kilowatt-hr x $.15 /kilowatt-hr = $12 36. 100 watt x 1 kilowatt/1,000 watts x 10 hrs. = 1 kilowatt-hr 21. 0 J 37. 1 kilowatt-hr x $.15 /kilowatt-hr =15 ¢ 22. 88 J 23. YES 38. 60 watt bulb NO 24. Work = F x d = ΔKE 39. harder because work is being done = ½ x 1000 kg x (31 m/s)2 = 480,500 J 25. F x d = ΔKE (60/20)2 = 32 x further = 9x further 26. F x d = ΔKE = ½ x 9.11 x 10 -31 x (1.90 x 10 6 m/s)2 = 1.64 x 10 -18 J 27. W = F x d so F = 7.0 x 10 4 J/ 2,800 m = 25 N 40. easier because no work is being done on the electrons 41. c) 42. Cosine was not used and was not needed since the angle between the applied force and the displacement of the cart was always zero degrees. 28. Efficiency = 32 J / 35J x 100 = 91.4 % 29. F x d = F x d d = (45 N x 125 cm)/ 25 N = 225 cm 30. M.A. = 225 cm / 125 cm = 1.8 31. F = (25 kg x 10 m/s2 x 40 cm)/ 80 cm =125 N 43. You would expect that the calculated values for work would be the same for any angle, since the elevation for each trial was identical and therefore according to conservation of energy, the amount of work to bring an object to a certain height is the same regardless of the path that is taken. 44. √2gh = 1.63 m/s 32. M.A. = 80 cm/ 40 cm = 2