Objectives for Chapter 10 – Energy, Work and Simple Machines Student Targets 403. I can identify kinetic energy as a function of velocity. 2. An object that has kinetic energy must be a. moving b. falling c. pretty d. elevated e. at rest

3. Which gives the correct relationship for kinetic energy? a. KE = mv c. KE = mv/2 2 b. KE = mv d. KE = mv2/2 4. An object that has kinetic energy must have A) acceleration. B) a force applied to maintain it. C) momentum. D) none of the above

404. I can calculate gravitational potential energy* and kinetic energy. 5. What’s the KE of a 100,000kg spaceship orbiting at 8,000m/s? a) 4 x 1013 J b) 3.2 x 1012 J c) 4 x 108J 406. I can identify that energy is transferred between different forms. 7. An arrow in a bow has 70 J of potential energy. Assuming no loss of energy due to heat or poor accounting procedures, how much kinetic energy will the arrow have after its shot and traveling in air? a. 140 J b. 70 J c. 50 J d. 35 J e. 0 J

407. I can solve problems using conservation of mechanical energy. 408. I can apply the mathematical definition of work as the product of Force and displacement. 10. How much net work is done by gravity on a rock that weighs 50 N that you carry horizontally across a 10 m room? a. 500 J b. 500 W c. 10 J d. 5 J e. 0 J \

11. It takes a net work of 40 J to push a box of physics papers 4 meters across a floor. Assuming the push is in the same direction as the box moved, what is the magnitude of the net force on the box of physics papers? a. 4 N b. 10 N c. 40 N d. 160 N e. none of these 12. T/F

When there is an angle between the force and the displacement, W = F d cosθ.

13. Clarice has a mass of 78 kg and climbs the schools stairs in 23.0 seconds. The school stairwell contains 41 stairs that are 18 cm tall each. How much work against gravity did Clarice do climbing up the stairs? a. 5641 J b. 576 J c. 564127J d. 245 J e. 764 J

409. I can identify situations of net positive work, negative work, zero work. 14. When friction slows down a ball, friction is doing: a) Positive Work b) Negative work c) zero work

410. I can identify work as a change in energy. 15. The amount of potential energy possessed by an elevated object is equal to A) the distance it is lifted. B) the work done in lifting it. C) the force needed to lift it. D) the value of the acceleration due to gravity. E) the power used to lift it.

OPRF Physics Custom Objectives Note: any objectives involving calculation of one variable imply the calculation of any other variable in the equation, depending on the given information. 10/11.1 Calculate power. 16. How much power is required to do 100 J of work on a 35 kg object in 2 seconds? a. 17.5 W b. 3500 W c. 200 W d. 50 W e. 100 W 17. Power equals work multiplied by time. a. True b. False

10.4 State SI units for work, energy, spring constant, and power. 21. The unit of energy is the watt.

a. True

b. False

22. The unit of power is the watt.

a. True

b. False

23. The unit of work is the Joule.

a. True

b. False

11.5 Calculate answers for hypothetical energy scenarios using the idea of proportionality. (e.g., if you double the velocity, what happens to the energy, etc) 24. If you lift two loads of equal weight up one story, how much work do you do compared to lifting just one load up one story? A) Four times as much B) One quarter as much C) Twice as much D) One half as much E) The same amount 25. If Nellie Newton pushes an object with three times the force for twice the distance, she does A) three times the work. B) six times the work. C) four times the work. D) the same work. 26. How much farther will a car traveling at 200 km/s skid than the same car traveling at 100 km/s? A) The same distance B) Five times as far C) Half as far D) Four times as far E) Twice as far 27. If a student pushes an object with twice the force for twice the distance, she does a. the same work b. twice the work c. four times the work d. eight times the work

28. How much MORE kinetic energy will a car traveling at 100 km/hr have then the same car traveling at 50 km/hr? a. five times as much b. four times as much c. twice as much d. the same e. half as much

Mechanical advantage Calculate the mechanical advantage of a lever that moves a 12,000N object 0.20m when a person applies a force of 910N over a distance of 3.00m. Calculate the ideal mechanical advantage for the system.

A student takes the following data for a spring. Find the work done on the spring and the spring constant. Displacement 0.0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0 2.3 2.5 2.8 3.0

Force 0.0 137.5 275.0 412.5 550.0 687.5 825.0 962.5 1100.0 1237.5 1375.0 1512.5 1650.0

Work Done by a Constant Force Choose from the following list:

2) Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do. A) Joel does 75% more work than Jerry. B) Joel does 50% more work than Jerry. C) Jerry does 50% more work than Joel. D) Neither of them do any work.

Answer: D Diff 2 3) You lift a 50. N physics book up in the air a distance of 1 m, at a constant velocity of 0.5 m/s. The work done by gravity is A) +50 J. B) -100 J. C) -50 J. D) zero. E) +100 J

Answer: C Diff: 2

4) Matthew pulls his little sister Sarah in a sled on an icy surface (assume no friction), with a force of 60.0 newtons at an angle of 37.0° upward from the horizontal. If he pulls her a distance of 12.0 m, the work he does is A) 0.333 kJ B) 720 J C) 575 J D) 433 J E) 185 J Answer: C Diff: 2 7) An auto is coasting on a level road. It weighs 10. kN. How much work is done by gravity as it moves horizontally 150. meters? Answer: zero (displacement is perpendicular to the force) Diff: 2 8) If there is no motion, can work be done on a system? A) yes, provided an outside force is applied B) yes, since motion is only relative C) no, since a system which is not moving has no kinetic energy D) no, because of the way work is defined Answer: D Diff:l Choose from the following list: (a) friction (b) J/s (c) dyne.cm (d) N-m (e) 550 ft.lb/s (f) mgy (g) 1/2 mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft.lb/s 9) Match joule to one of the choices above. Answer: (d) N-m Diff: 1

11) When you lift a 12. ounce (3N) beverage can from the table top to your mouth, you do approximately how much work? A) 1 Calorie B) 1 Wall C) 1 Kw-h D) 1 Joule E) 1 erg Answer: D Diff:2 13) You throw a ball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down. A) Work up is -, and the work down is -. B) Work up is +, and the work down is +. C) Work up is -, and the work down is +. D) Work up is +, and the work down is-. Answer: C Diff:2 Work Done by a Variable Force 1) A 10. kg mass, hung onto a spring, causes the spring to stretch 2.0 cm. The spring constant is A) 5.0 N/cm B) 49 N/cm C) 0.20 N/cm D) 20. N/m E) 0.0020 N/cm Answer: B Diff:2 5) The area under the curve, on a Force vs. position (F-x) graph, represents A) work. B) efficiency. C) kinetic energy. D) power. E) friction.

Answer: A Diff 1

6) The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown on the graph above. How much work did the squirrel do during that 10. s? A) 12.5 J B) 50. J C) 25. J D) 22. J E) zero Answer: C Diff: 2 7) The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown on the graph above. What was the average power exerted by the squirrel? A) zero B) 1.3 W C) 2.5 W D) 2.2 W E) 5.0 W Answer: C Diff: 2

9) Consider a 0.002 gram mass hung from a spring. When an additional 15. kg is added, the equilibrium position changes by 20. cm. (a) What is the spring constant? (b) How much work is done on the spring? Difficult – Draw graph (c) If 30. kg are added, by how much will the equilibrium position change? Answer: (a) 0.74 x 103 N/m (b) 15. J (c) 40. cm Diff:3

8) The resultant force you exert while pressing a key on the keyboard of your new computer, for a 1.0-s period, is plotted on the graph, shown.

How much work did you do during this 1-s interval? A) zero B) 50. J C) -25. J D) 12.5 J E) 22. J Answer: A Diff: 2 10) Daisy raises 10.kg to a height of 2.5 meters in 2.0 seconds. (a) How much work did she do? (b) How much power was expended? (c) If she raises it in 1.0s rather than 2.0s, how do the work and power change? Answer: (a) 0.25 kJ (b) 0.13 kW (c) same work but power doubles Diff:3 11) Consider a plot of the applied force (F) vs, displacement (x) for an ideal elastic spring. The slope of the curve would be A) the spring constant. B) the reciprocal of the spring constant. C) the acceleration of gravity. D) the reciprocal of the acceleration of gravity. Answer: A Diff:2 The Work-Energy Theorem: Kinetic Energy 1) A driver, traveling at 22. m/s, slows down her 1500. kg car to stop for a red light. What work is done by the friction force against the wheels? Answer: 3.6 x 105 Joules Diff:2

Choose from the following list: (a) friction (b) J/s (c) dyne-cm (d) N.m (e) 550 ft.lb/s (f) mgy (g) 1/2 mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft-lb (I) -kx (m) weight (n) ft-lb/s 2) Match kinetic energy to one of choices above. Answer: (g) 1/2 mv2 Diff: 1 3) The work energy theorem says A) the net work done is equal to the initial kinetic energy less the final energy. B) the net work done plus the final kinetic energy is the initial kinetic energy. C) the net work done plus the initial kinetic energy is the final kinetic energy. D) the net work done minus the initial kinetic energy is the final kinetic energy. E) final kinetic energy plus the net work done is the initial kinetic energy. Answer: C Diff: 2 4) Car J moves twice as fast as car K, and car J has half the mass of car K. The kinetic energy of car J, compared to car K is A) 4 to 1. B) 2 to 1. C) the same. D) 42 to 1. E) 1 to 2. Answer: B Diff: 2 5) If both the mass and the velocity of a ball are tripled, the kinetic energy is increased by a factor of A) 18. B) 81. C) 6. D) 9. E) 27. Answer: E

Diff: 2

6) Is more work required to increase a car's speed from rest to 30 mph, or from 50 mph to 60 mph? Answer: 50 to 60 mph Diff:2 7) Kinetic energy is proportional to speed. Answer: FALSE Diff: 1

9) A truck weighs twice as much as a car, and is moving at twice the speed of the car. Which statement is true about the truck's kinetic energy (KE) compared to that of the car? A) The truck has 4 times the KE of the car. B) All that can be said is that the truck has more KE. C) The truck has twice the KE of the car. D) The truck has 8 times the KE of the car. E) The truck has 2 times the KE of the car. Answer: D Diff: 2 Choose from the following list: (a) friction (b) J/s (c) dyne-cm (d) N-m (e) 550 ft.lb/s (f) mgy (g) 1/2 mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft-lb (I) -kx (m) weight (n) ft-lb/s

3) Match spring constant to one of the choices above. Answer: (i) N/m Diff: 1

8) On the accompanying diagram of a pendulum, at what position is the kinetic energy maximum? A) A B) B C) C

Answer: A Diff: 2

13) On a plot of F vs. x, what represents the work done by the force F? A) the slope of the curve B) the length of the curve C) the area under the curve D) the product of the maximum force times the maximum x E) the maximum F times minimum x Answer: C Diff: 2 9) A "machine" multiplies (increases) A) time. B) energy. C) work. D) force. E) power. Answer: D Diff: 1 10) You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions? A) It would have skidded 4 times farther. B) It would have skidded twice as far. C) It would have skidded.J2 times farther. D) It is impossible to tell from the information given. Answer: A Diff: 2

14) A 4-kg mass moving with speed 2 m/s, and a 2-kg mass moving with a speed of 4 m/s, are gliding over a horizontal frictionless surface. Both objects encounter the same horizontal force, which directly opposes their motion, and are brought to rest by it. Which statement correctly describes the situation? A) Both masses travel the same distance before stopping. B) The 2-kg mass travels twice as far as the 4-kg mass before stopping. C) The 2-kg mass travels farther, but not necessarily twice as far. D) The 4-kg mass travels twice as far as the 2-kg mass before stopping. E) The 4-kg mass loses more kinetic energy than the 2-kg mass. Answer: B Diff: 2 23) A container of water is lifted vertically 3.0 m, then returned to its original position. If the total weight is 30. N, how much work was done? A) 0.18 kJ B) 45 J C) 90 J D) No work was done. E) 0.90 kJ Answer: D Diff 2 Power Choose from the following list: (a) friction (b) J/s (c) dyne-cm (d) N-m (e) 550 ft-lb/s (f) mgy (g) 1/2 mv2 (h) dimensionless (i) N/m (j) 3.6 MJ (k) ft-lb (I) -kx (m) weight (n) ft-lb/s 2) Match efficiency to one of the choices above. Answer: (h) dimensionless Diff: 1 3) Match watt to one of the choices above. Answer: (b) J/s Diff: 1

7) Compared to yesterday, you did 3 times the work in one-third the time. To do so, your power output must have been A) the same as yesterday's power output. B) one-third of yesterday's power output. C) 3 times yesterday's power output. D) 9 times yesterday's power output. E) 34 times yesterday's power output. Answer: D Diff: 2 13) A roofer lifts supplies a height of 20. m with a hand-operated winch. How long would it take him to lift a 200. kg load, if the winch has an efficiency of 90%, and the rate at which the winch can do work is 600W? Answer: 73. seconds Diff: 2 15) Water flows over a waterfall 20.m high, at the rate of 4.0 x 10 4 kg/s. If this water powers an electric generator with a 40% efficiency, how many watts of electric power can be supplied? Answer: 3.1MW Diff: 2 18) Lisa runs up 4 flights of stairs in 22. seconds. She weighs 510. Newtons. If each flight rises 310.cm: (a) What was her work? (b) What average power (watts) was required during the 22. s? Answer: (a) 6.32 kJ (b) 287. watts Diff:3 19) A cyclist does work at the rate of 500.W while riding. With how much average horizontal force does the wheel push when she is traveling at 10. m/s? Answer: 50. N Diff:2 21) Assuming muscles are 20% efficient, at what rate is a 60. kg boy using energy when he runs up a flight of stairs 10.m high, in 8.0 s? Answer: 3.7 kW Diff: 2

Chapter 11 Review NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.

5) If the roller coaster leaves point Q from rest, how fast is it traveling at point R? A) 0.98 km/s B) 31 m/s C) 22 m/s D) 0.49 km/s E) 51 m/s Answer: B Diff: 2 11) A toy rocket, weighing 10. N, blasts off from ground level. At the exact top of its trajectory, its energy is 140.J. To what vertical height does it rise? A) 1.4m B) 14.m C) 12.m D) 0.12 km E) 1.4 km Answer: B Diff: 2 18) A leaf falls from a tree. Compare its Kinetic energy KE to its potential energy PE. A) KE increases, and PE decreases. B) KE decreases, and PE increases. C) KE decreases, and PE decreases. D) KE increases, and PE increases. E) KE and PE remain constant. Answer: A Diff:1 20) Is it possible for a system to have negative potential energy? A) Yes, as long as the total energy is positive. B) Yes, since the choice of the zero of potential energy is arbitrary. C) No, because this would have no physical meaning. D) No, because the kinetic energy of a system must equal its potential energy.

Answer: B Diff: 2 NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.

16) How fast must the coaster be moving at P in order to coast to a stop at Q? A) 9.8 m/s B) 31. m/s C) 22. m/s D) 0.49 km/s E) 0.98 km/s Answer: B Diff: 2 21) King Kong falls from the top of the Empire State Building, through the air (air friction is present), to the ground below. How does his kinetic energy (KE) just before striking the ground compare to his potential energy (PE) at the top of the building? A) KE is equal to PE. B) It is impossible to tell. C) KE is less than PE. D) KE is greater than PE. Answer: C Diff:2 22) A skier, of mass 60. kg, pushes off the top of a hill with an initial speed of 4.0 mIs. How fast will she be moving after dropping 10.m in elevation? (ignore friction) A) 0.20 km/s B) 15. m/s C) 10. m/s D) 0.15 km/s E) 49. m/s Answer: B Diff:2

23) A container of water is lifted vertically 3.0 m, then returned to its original position. If the total weight is 30. N, how much work was done? A) 0.18 kJ B) 45 J C) 90 J D) No work was done. E) 0.90 kJ Answer: D Diff 2 24) A 1.0 kg flashlight falls to the floor. At the point during its fall when it is 0.70 m above the floor, its potential energy exactly equals its kinetic energy. How fast is it moving? A) 3.7 m/s B) 6.9 m/s C) 14 m/s D) 45 m/s E) 9.8 m/s Answer: A Diff 2 You have a 12.5g popper that is 1.0cm tall when turned inside out. It reaches 1.00m at the top of its trajectory. Assume no friction. A. B. C. D. E. F.

What type of energy does the popper have when it is barely off the table? What is the potential energy at the top of its arc? What is the kinetic energy at the top of its trajectory? What is the kinetic energy when the popper is barely off the table? What is the work done by the popper? What is the force of the popper on the table?

Answer: A. kinetic B. 0.1225J C. 0 J D. 0.1225J E. 0.1225J F. 12.25N 1. Which type of energy is associated with a body’s height above the ground? a. thermal energy b. elastic potential energy c. gravitational potential energy d. rest energy Answer: C

3. Which gives the correct relationship for kinetic energy? a. KE = mv 2 b. KE = mv c. KE = mv/2 d. KE = mv2/2 Answer: D 4. An object that has kinetic energy must have A) acceleration. B) a force applied to maintain it. C) momentum. D) none of the above Answer: C

404. I can calculate gravitational potential energy* and kinetic energy. 5. What’s the KE of a 100,000kg spaceship orbiting at 8,000m/s? a) 4 x 1013 J b) 3.2 x 1012 J c) 4 x 108J Answer: B 405. I can identify an isolated system and analyze it. 6. A gymnast falls from a height onto a trampoline. For a moment on the trampoline, both the gymnast’s kinetic energy and gravitational potential energy are zero. How is most of the gymnast’s mechanical energy stored for that moment? a. b. c. d.

Rest energy Chemical potential energy Elastic potential energy Thermal energy

Answer: C (in the springs of the trampoline) 406. I can identify that energy is transferred between different forms. 7. An arrow in a bow has 70 J of potential energy. Assuming no loss of energy due to heat or poor accounting procedures, how much kinetic energy will the arrow have after its shot and traveling in air? a. 140 J b. 70 J c. 50 J d. 35 J e. 0 J Answer: B

8. If I drop a rock from a cliff it starts off being primarily ________ and right before striking the ground it is mainly______ a. Kinetic; Gravitational potential b. Gravitational potential; Kinetic c. Gravitational; Elastic

Answer: B 407. I can solve problems using conservation of mechanical energy. 9. As a pendulum swings back and forth. A) at the end points of its swing, its energy is all potential. B) kinetic energy is transformed into potential energy. C) at the lowest part of its swing, it has maximum energy. D) potential energy is transformed into kinetic energy. E) all of the above Answer: E

408. I can apply the mathematical definition of work as the product of Force and displacement. 409. I can identify situations of net positive work, negative work, zero work. 14. When friction slows down a ball, friction is doing: a) Positive Work b) Negative work c) zero work Answer: B

410. I can identify work as a change in energy. 15. The amount of potential energy possessed by an elevated object is equal to A) the distance it is lifted. B) the work done in lifting it. C) the force needed to lift it. D) the value of the acceleration due to gravity. E) the power used to lift it. Answer: C

OPRF Physics Custom Objectives Note: any objectives involving calculation of one variable imply the calculation of any other variable in the equation, depending on the given information. 11.1 Calculate power. 11.2 Apply conservation of energy to various problems, taking non-conservative forces into account. 18. Energy transforms from one form to another with no net loss or gain if it is a closed isolated system. a. T or b. F? Answer: T (net for the entire system)

19. The American Falcon roller coaster has a mass of 2000 kg and its tallest hill, the first hill, is 24 meters above the ground. The coaster races down the first hill then up to the top of the second hill, which is 3 meters above the ground. Assuming that we lose no kinetic energy to friction, how fast is the American Falcon going at the top of this second hill? a. 9.8 m/s b. 21.7 m/s c. 7.7 m/s d. 15.4 m/s e. 20.3 m/s Answer: E. 20.3 m/s

11.3 State and/or recognize conditions of validity for conservation of mechanical energy of a system (must know definition of a closed system). 20. In a closed system, no objects enter or leave the system.

a. True b. False Answer: A 11.4 State SI units for work, energy, spring constant, and power. 11.5 Calculate answers for hypothetical energy scenarios using the idea of proportionality. (e.g., if you double the velocity, what happens to the energy, etc)

These problems are more difficult. Good practice, if you know your stuff. 14) A 4-kg mass moving with speed 2 m/s, and a 2-kg mass moving with a speed of 4 m/s, are gliding over a horizontal frictionless surface. Both objects encounter the same horizontal force, which directly opposes their motion, and are brought to rest by it. Which statement correctly describes the situation? A) Both masses travel the same distance before stopping. B) The 2-kg mass travels twice as far as the 4-kg mass before stopping. C) The 2-kg mass travels farther, but not necessarily twice as far. D) The 4-kg mass travels twice as far as the 2-kg mass before stopping. E) The 4-kg mass loses more kinetic energy than the 2-kg mass.

Answer: B Diff: 2

NOTE: The following question(s) refer(s) to the Cyclone, the famous roller coaster ride at Coney Island, shown in the sketch. Assume no friction.

15) If the roller coaster leaves point Q from rest, what is its speed at point S (at the top of the 25. m peak) compared to its speed at point R? A) zero B) 1/ C) D) 2 E) 4

Answer: B Diff: 2 19) A 30. N stone is dropped from a height of 10. m, and strikes the ground with a velocity of 13.m/s. What average force of air friction acts on it as it falls? A) 7.2 N B) 2.9 N C) 1.2 N D) 4.1 N E) 0.13 KN

Answer: D Diff: 2