AP MIDTERM SAMPLE. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

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1 Name: Class: _ Date: _ ID: B AP MIDTERM SAMPLE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The radius of Earth is m. Express this measurement in km in scientific notation with the correct number of significant digits. a km c km b km d km 2. Calculate the following, and express the answer in scientific notation with the correct number of significant figures: a c b d Calculate the following, and express the answer in scientific notation with the correct number of significant figures: a c b. 290 d Calculate the following, and express the answer in scientific notation with the correct number of significant figures: ( )( ) a c b d Which expression has the same dimensions as an expression yielding a value for acceleration (m/s 2 )? (Δv has units of m/s.) a. (Δv) 2 Δt c. Δv (Δx) 2 b. Δv (Δt) 2 d. (Δv) 2 Δx 6. Which of the following expressions gives units of kg m 2 s 2? a. m (Δx) 2 (Δt) 2 c. (Δt) 2 m (Δx) 2 b. m 2 Δx (Δt) 2 d. m (Δx) 2 Δt 7. If the change in position Δx is related to velocity v (with units of m/s) in the equation Δx = Av, the constant A has which dimension? a. m 2 c. s b. m d. m/s 2 8. If a is acceleration (m/s 2 ), Δv is change in velocity (m/s), Δx is change in position (m), and Δt is the time interval (s), which equation is not dimensionally correct? a. Δt 2 = 2Δx a c. Δt = Δx v b. Δv = a Δt d. a = v 2 Δx 1

2 Name: ID: B 9. For the winter, a duck flies 10.0 m/s due south against a gust of wind with a speed of 2.5 m/s. What is the resultant velocity of the duck? a m/s south c. 7.5 m/s south b m/s south d. 7.5 m/s south 10. An ant on a picnic table travels cm eastward, then 25 cm northward, and finally 15 cm westward. What is the magnitude of the ant s displacement relative to its original position? a. 52 cm c. 70 cm b. 29 cm d. 57 cm 11. A late traveler rushes to catch a plane, pulling a suitcase with a force directed 30.0 above the horizontal. If the horizontal component of the force on the suitcase is 60.6 N, what is the force exerted on the handle? a N c N b N d N 12. A waitperson carrying a tray with a platter on it tips the tray at an angle of 12 below the horizontal. If the gravitational force on the platter is 5.0 N, what is the magnitude of the force parallel to the tray that tends to cause the platter to slide down the tray? (Disregard friction.) a N c. 5.0 N b. 1.0 N d. 4.9 N 13. A net force of 6.8 N accelerates a 31 kg scooter across a level parking lot. What is the magnitude of the scooter s acceleration? a. 3.2 m/s 2 c m/s 2 b m/s 2 d. 4.6 m/s An airplane with a mass of kg tows a glider with a mass of kg. If the airplane propellers provide a net forward thrust of N, what is the acceleration of the glider? (Disregard friction.) a m/s 2 c m/s 2 b m/s 2 d m/s A sled weighing N is held in place on a frictionless 20.0 slope by a rope attached to a stake at the top. The rope is parallel to the slope. What is the normal force of the slope acting on the sled? a. 94 N c. 34 N b. 37 N d. 47 N 16. There are six books in a stack, and each book weighs 5 N. The coefficient of static friction between the books is 0.2. With what horizontal force must one push to start sliding the top five books off the bottom one? a. 1 N c. 5 N b. 3 N d. 7 N 17. A construction worker pushes a wheelbarrow 5.0 m with a horizontal force of 50.0 N. How much work is done by the worker on the wheelbarrow? a. 10 J c. 250 J b J d. 55 J 2

3 Name: ID: B 18. A horizontal force of 200 N is applied to move a 55 kg television set across a 10 m level surface. What is the work done by the 200 N force on the television set? a. 550 J c J b J d J 19. A child pulls a balloon for 12 m with a force of 1.0 N at an angle 60 below horizontal. How much work does the child do on the balloon? a. 6.0 J c. 10 J b. 12 J d. 6.0 J 20. What is the kinetic energy of a kg baseball thrown at 40.0 m/s? a J c. 216 J b J d. 108 J 21. What is the potential energy of a 1.0 kg mass 1.0 m above the ground? a. 9.8 J c. 10 J b. 1.0 J d. 96 J 22. How much elastic potential energy is stored in a bungee cord with a spring constant of 10.0 N/m when the cord is stretched 2.00 m? a J c J b. 200 J d J 23. A 3.00 kg toy falls from a height of 1.00 m. What will the kinetic energy of the toy be just before the toy hits the ground? (Assume no air resistance and that g = 9.81 m/s 2.) a J c. 9.8 J b J d. 294 J 24. How much power is required to lift a 2.0 kg mass at a speed of 2.0 m/s? a. 2.0 J c. 4.0 J b. 9.8 J d. 39 J 25. What is the average power supplied by a 60.0 kg person running up a flight of stairs a vertical distance of 4.0 m in 4.2 s? a. 57 W c. 560 W b. 670 W d. 240 W 26. Which of the following has the greatest power output? a. a crane that lifts a N beam at a speed of 1.2 m/s b. a mechanic s lift that raises a N car 2.1 m in 12 s c. a car engine that does J of work in 5.0 s d. a weightlifter who lifts a 250 N weight 2.1 m in 3.0 s Short Answer 27. Convert km to decimeters using scientific notation. 28. Convert 1 µm to meters using scientific notation. 29. Convert g to kilograms using scientific notation. 30. Convert m to millimeters using scientific notation. 3

4 Name: ID: B 31. Construct a graph of position versus time of a jogger, using the data in the table above. Explain how the graph indicates that the jogger s speed is constant. 32. Construct a graph of position versus time of a jogger, using the data in the table above. What is the average velocity of the jogger? 33. A motorized scooter starts from rest and accelerates for 4 s at 2 m/s 2. It continues at a constant speed for 6 s. Graph the scooter s velocity versus time. What is the scooter s average velocity for the interval 0 4 s? 34. What is the kinetic energy of a kg car traveling at 25 m/s? Problem 35. Calculate the following, expressing the answer in scientific notation with the correct number of significant figures: ˆ

5 Name: ID: B 36. A horse trots past a fencepost located 12 m to the left of a gatepost. It then passes another fencepost located 24 m to the right of the gatepost 11 s later. What is the average velocity of the horse? 37. The graph above shows displacement versus time. What is the average velocity for line A? 38. The graph above shows displacement versus time. What is the average velocity for line B? 39. The graph above shows displacement versus time. What is the average velocity for line C? 40. The graph above shows the motion of a cat. What is the cat s average velocity during the time interval s? 41. A shopping cart is given an initial velocity of 2.0 m/s and undergoes a constant acceleration of 3.0 m/s 2. What is the magnitude of the cart s displacement after the first 4.0 s of its motion? 5

6 Name: ID: B 42. A skater glides off a frozen pond onto a patch of ground at a speed of 1.8 m/s. Here she is slowed at a constant rate of 3.00 m/s 2. How fast is the skater moving when she has slid 0.37 m across the ground? 43. A sports car traveling at 27.8 m/s slows at a constant rate to a stop in 8.00 s. What is the displacement of the sports car in this time interval? 44. Human reaction time is usually about 0.20 s. If your lab partner holds a ruler between your finger and thumb and releases it from rest without warning, how far can you expect the ruler to fall before you catch it? (Disregard air resistance. a = g = 9.81 m/s 2.) 45. A rock is thrown downward from the top of a cliff with an initial speed of 12 m/s. If the rock hits the ground after 2.0 s, what is the height of the cliff? (Disregard air resistance. a = g = 9.81 m/s 2.) 46. A rock is thrown straight upward with an initial velocity of 24.5 m/s where the acceleration due to gravity has a magnitude of 9.81 m/s 2. What is the rock s displacement after 1.00 s? 47. A lightning bug flies at a velocity of 0.25 m/s due east toward another lightning bug seen off in the distance. A light easterly breeze blows on the bug at a velocity of 0.25 m/s. What is the resultant velocity of the lightning bug? 48. A jogger runs 10.0 blocks due east, 5.0 blocks due south, and another 2.0 blocks due east. Assume all blocks are of equal size. Use the graphical method to find the magnitude of the jogger s net displacement. 49. A cave explorer travels 3.0 m eastward, then 2.5 m northward, and finally 15.0 m westward. Use the graphical method to find the magnitude of the net displacement. 50. An airplane flying at 120 km/h due west moves into a region where the wind is blowing at 40 km/h due east. If the plane s original vector velocity is vplane, what is the expression for the plane s resulting velocity in terms of vplane? 51. A dog walks 28 steps north and then walks 55 steps west to bury a bone. If the dog walks back to the starting point in a straight line, how many steps will the dog take? Use the graphical method to find the magnitude of the net displacement. 52. A quarterback takes the ball from the line of scrimmage and runs backward for m. He then runs sideways, parallel to the line of scrimmage, for 15 m. Next, he throws the ball forward m, perpendicular to the line of scrimmage. The receiver is tackled immediately. How far is the football displaced from its original position? 53. A string attached to an airborne kite was maintained at an angle of 40.0 with the ground. If 120 m of string was reeled in to return the kite back to the ground, what was the horizontal displacement of the kite? (Assume the kite string did not sag.) 54. An athlete runs 110 m across a level field at an angle of 30.0 north of east. What is the north component of this displacement? 55. A small airplane flies at a velocity of 145 km/h toward the south as observed by a person on the ground. The airplane pilot measures an air velocity of 172 km/h south. What is the velocity of the wind that affects the plane? 6

7 Name: ID: B 56. In a game of tug-of-war, a rope is pulled by a force of 102 N to the right and by a force of 75 N to the left. What is the magnitude and direction of the net horizontal force on the rope? 57. Two ice-hockey players simultaneously strike a puck with their sticks. The stick of one player exerts an eastward force on the puck of 12 N. The other player s stick exerts a northward force of 15 N on the puck. Assuming that there is no frictional force between the puck and the ice, what is the magnitude of the net horizontal force on the puck? 58. A package of meteorological instruments is held aloft by a balloon that exerts an upward force of 634 N on the package. The gravitational force acting on the package is 365 N. What is the magnitude and direction of the force that a scientist must exert on a rope attached to package to keep it from rising? 59. A wagon having a mass of 32 kg is accelerated across a level road at 0.50 m/s 2. What net force acts on the wagon horizontally? 60. A farmhand attaches a 25 kg bale of hay to one end of a rope passing over a frictionless pulley connected to a beam in the hay barn. Another farmhand then pulls down on the opposite end of the rope with a force of 277 N. Ignoring the mass of the rope, what will be the magnitude and direction of the bale s acceleration if the gravitational force acting on it is 245 N? 61. Basking in the sun, a 1.10 kg lizard lies on a flat rock tilted at an angle of 15.0 with respect to the horizontal. What is the magnitude of the normal force exerted by the rock on the lizard? 62. A three-tiered birthday cake rests on a table. From bottom to top, the cake tiers weigh 16 N, 9 N, and 5 N, respectively. What is the magnitude and direction of the normal force acting on the second tier? 63. A row of six 1.0 N wooden blocks is being pushed across a tabletop at a constant speed by a toy tractor that exerts a force of 1.3 N on the row. What is the coefficient of kinetic friction between the wooden blocks and the tabletop? 64. A waitperson pushes the bottom of a glass tumbler full of water across a tabletop at constant speed. The tumbler and its contents have a mass of 0.70 kg, and the coefficient of kinetic friction for the surfaces in contact is What force does the waitperson exert on the glass? g = 9.81 m/s 2 ) 65. How much work is done on a bookshelf being pulled 5.00 m at an angle of 37.0 from the horizontal? The magnitude of the component of the force that does the work is 43.0 N. 66. A skier with a mass of 88 kg hits a ramp of snow at 16 m/s and becomes airborne. At the highest point of flight, the skier is 3.7 m above the ground. What is the skier s gravitational potential energy at this point? 67. An 80.0 kg climber climbs to the top of Mount Everest, which has a peak height of 8848 m above sea level. What is the climber s potential energy with respect to sea level? 68. A scale contains a spring with a spring constant of 275 N/m. Placing a mass on the scale causes the spring to be compressed by 3.25 cm. Calculate the elastic potential energy stored in the spring. 69. A pendulum with a mass of 1 kg is released from a height of 1.5 cm above the height of its resting position. How fast will the pendulum be moving when it passes through the lowest point of its swing? 70. What is the average power output of a weightlifter who can lift 250 kg a height of 2.0 m in 2.0 s? 7

8 AP MIDTERM SAMPLE Answer Section MULTIPLE CHOICE 1. ANS: C ( m) 1 km 1000 m ˆ = km PTS: 1 DIF: IIIA OBJ: ANS: A Answer rounds to 58 and is written as in scientific notation. PTS: 1 DIF: IIIA OBJ: ANS: A ( 10.5) ( 8.8) ( 3.14) = The answer rounds to 290 and is written as in scientific notation. PTS: 1 DIF: IIIA OBJ: ANS: C ( ) ˆ = ( 0.86 ) 3 ˆ = 3784 The answer rounds to 3800 and is written as in scientific notation. PTS: 1 DIF: IIIA OBJ: ANS: D ( Δv) 2 Δx = ( m/s) 2 m = m2 /s 2 m = m/s 2 PTS: 1 DIF: IIIA OBJ:

9 6. ANS: A m ( Δx) 2 = kg ( Δt) 2 ˆ m 2 ˆ s 2 ˆ = kgm 2 /s 2 PTS: 1 DIF: IIIA OBJ: ANS: C Δx = Av Rearrange the equation to solve for A and substitute units. A = Δx v = m m/s = s PTS: 1 DIF: IIIA OBJ: ANS: B Does Δv = a Δt? Substitute units into the right side of the equation. a Δt = m/s 2 s = m s 2 ˆ ( s) 1 s 1 ˆ s ˆ = m s 3 Substituting units into both sides of the equation yields the following result: m s m s 3 PTS: 1 DIF: IIIA OBJ: ANS: D v 1 = 10.0 m/s south v 2 = 2.5 m/s north v R = v 1 v 2 = 10.0 m/s 2.5 m/s = 7.5 m/s vr = 7.5 m/s south PTS: 1 DIF: IIIA OBJ:

10 10. ANS: B Δx 1 = cm Δy 1 = 25 cm Δx 2 = 15 cm Δx tot = Δx 1 + Δx 2 = ( cm) + ( 15 cm) = 15 cm Δy tot = Δy 1 = 25 cm d 2 = (Δx tot ) 2 + (Δy tot ) 2 d = (Δx tot ) 2 + (Δy tot ) 2 = (15 cm) 2 + (25 cm) 2 d = 29 cm PTS: 1 DIF: IIIA OBJ: ANS: C F y = 60.0 N θ = 30.0 cosθ = F y F F = F y cosθ = 60.6 N cos 30.0 = 70.0 N PTS: 1 DIF: IIIA OBJ: ANS: B F g = 5.0 N α = 12 θ = = 78 ΣF x = F g, x = F g cosθ = (5.0 N)(cos78 ) = 1.0 N PTS: 1 DIF: IIIA OBJ:

11 13. ANS: C F applied = 6.8 N m = 31 kg F net = a x = F applied m F x = F applied = ma x = 6.8 N 31 kg = 0.22 m/s 2 PTS: 1 DIF: IIIA OBJ: ANS: D Fnet = N, forward m 1 = kg m 2 = kg F net = ma = (m 1 + m 2 )a a = F net m 1 + m 2 = N ( kg) + ( kg) = 2.00 m/s 2 PTS: 1 DIF: IIIA OBJ: ANS: A F g = N θ = 20.0 ΣF y = F n F g, y = 0 F n = F g, y = F g cosθ = ( N)(cos 20.0 ) = 94 N PTS: 1 DIF: IIIA OBJ:

12 16. ANS: C F g, book = 5 N µ s = 0.2 ΣF x = F applied F s,max = 0 F applied = F s,max = µ s F n = µ s F g F g = ( 5Ν + 5Ν + 5Ν + 5Ν + 5Ν) = 25Ν F applied = ( 0.2) ( 25Ν) = 5Ν PTS: 1 DIF: IIIA OBJ: ANS: C J F = 50.0 N d = 5.0 m W = Fd = ( 50.0 N) ( 5.0 m) = J PTS: 1 DIF: IIIA OBJ: ANS: B F = 200 N d = 10 m W = Fd = ( 200 N) ( 10 m) = J PTS: 1 DIF: IIIA OBJ:

13 19. ANS: A F = 1.0 N d = 12 m θ = 60 È W = Fdcosθ = ( 1.0 N) ( 12 m) ÎÍ cos( 60 ) = 6.0 J PTS: 1 DIF: IIIA OBJ: ANS: D m = kg v = 40.0 m/s KE = 1 2 mv2 = 1 2 (0.135kg)(40.0m / s) 2 = 108J PTS: 1 DIF: IIIA OBJ: ANS: A m = 1.0 kg h = 1.0 m g = 9.81 m/s 2 PE = mgh = 1.0 kgˆ 9.81 m/s 2 ˆ ( 1.0 m) = 9.8 J PTS: 1 DIF: IIIA OBJ:

14 22. ANS: C k = 10.0 N/m x = 2.00 m PE = 1 2 kx2 = 1 2 ( 10.0 N/m) ( 2.00 m) 2 = 20.0 J PTS: 1 DIF: IIIA OBJ: ANS: A m = 3.00 kg h = 1.00 m g = 9.81 m/s 2 KE f = PE g, i = mgh = 3.00 kgˆ 9.81 m/s 2 ˆ ( 1.00 m) = 29.4 J PTS: 1 DIF: IIIA OBJ: ANS: D m = 2.0 kg v = 2.0 m/s g = 9.81 m/s 2 P = Fv = mgv = 2.0 kgˆ 9.81 m/s 2 ˆ ( 2.0 m/s) = 39 J/s PTS: 1 DIF: IIIA OBJ:

15 25. ANS: C m = 60.0 kg d = 4.0 m Δt = 4.2 s g = 9.81 m/s 2 P = W Δt = Fd Δt = mgd Δt = 60.0 kg ˆ 9.81 m/s s ˆ ( 4.0 m) = W PTS: 1 DIF: IIIA OBJ:

16 26. ANS: A a: F = 250 N d = 2.1 m Δt = 3.0 s b: F = N d = 2.1 m Δt = 12 s c: W = J Δt = 3.0 s d: F = N v = 1.2 m/s P = W Δt = Fd Δt = Fv P a = Fd Δt = ( 250 N) ( 2.1 m) = J 2.0 s P b = Fd ˆ N Δt = ( 2.1 m) = J 12 s P c = W ˆ J Δt = = J 5.0 s P d = Fv = ˆ N ( 1.2 m/s ) = J P d > P b > P a > P c PTS: 1 DIF: IIIA OBJ:

17 SHORT ANSWER 27. ANS: dm ˆ km 10 4 dm 1 km ˆ = dm = dm PTS: 1 DIF: IIIA OBJ: ANS: m 10 1 µm ˆ 6 ˆ m 1 µm = m PTS: 1 DIF: IIIA OBJ: ANS: kg ˆ 1 kg ˆ g 10 3 g = kg PTS: 1 DIF: IIIA OBJ: ANS: mm ˆ m 10 3 mm 1 m ˆ = mm PTS: 1 DIF: IIIA OBJ:

18 31. ANS: The jogger is moving at a constant speed because the position versus time graph is a straight line with a positive slope. PTS: 1 DIF: IIIA OBJ:

19 32. ANS: m/s x i = 2.8 m x f = 5.2 m t i = 2.0 s t f = 8.0 s v avg = Δx Δt = x f x i t f t i = 5.2 m 2.8 m 8.0 s 2.0 s = 2.4 m 6.0 s = 0.40 m/s PTS: 1 DIF: IIIA OBJ:

20 33. ANS: +2.0 m/s v i = 0.0 m/s v f = 4.0 m/s v avg = v i + v f 2 = 0.0 m/s m/s 2 = 2.0 m/s PTS: 1 DIF: IIIA OBJ: ANS: J m = kg v = 25 m/s KE = 1 2 mv2 = ˆ kg ( 25 m/s ) 2 = J PTS: 1 DIF: IIIA OBJ:

21 PROBLEM 35. ANS: ˆ ˆ = ( 8.86) ˆ = PTS: 1 DIF: IIIA OBJ: ANS: 3.3 m/s, to the right x i = 12 m x f = 24 m Δt = 11 s v avg = Δx Δt = x x f i Δt = ( 24 m) ( 12 m) 11 s = 3.3 m/s,to the right PTS: 1 DIF: IIIA OBJ: ANS: 3.0 m/s x i = 0.0 m x f = 9.0 m t i = 0.0 s t f = 3.0 s v avg = Δx Δt = x f x i t f t i = 9.0 m 0.0 m 3.0 s 0.0 s = 3.0 m/s PTS: 1 DIF: IIIA OBJ:

22 38. ANS: 1.0 m/s x i = 0.0 m x f = 3.0 m t i = 0.0 s t f = 3.0 s v avg = Δx Δt = x f x i t f t i = 3.0 m 0.0 m 3.0 s 0.0 s = 1.0 m/s PTS: 1 DIF: IIIA OBJ: ANS: 0.33 m/s x i = 0.0 m x f = 3.0 m t i = 0.0 s t f = 9.0 s v avg = Δx Δt = x f x i t f t i = 3.0 m 0.0 m 9.0 s 0.0 s = 0.33 m/s PTS: 1 DIF: IIIA OBJ:

23 40. ANS: m/s, south x i = 2.0 m x f = 0.5 m t i = 0.0 s t f = 20.0 s v avg = Δx Δt = x f x i t f t i = 0.5 m 2.0 m 20.0 s 0.0 s = 1.5 m 20.0 s = m/s v avg = m/s,south PTS: 1 DIF: IIIA OBJ: ANS: 32 m v i = 2.0 m/s a = 3.0 m/s 2 Δt = 4.0 s Δx = v i Δt a(δt) 2 Δx = (2.0 m/s)(4.0 s) (3.0 m/s 2 )(4.0 s) 2 = 8.0 m + 24 m Δx = 32 m PTS: 1 DIF: IIIA OBJ:

24 42. ANS: 1.0 m/s v i = 1.8 m/s a = 3.00 m/s 2 Δx = 0.37 m v f 2 = v i 2 + 2aΔx v f = v i 2 + 2aΔx = (1.8 m/s) 2 + 2( 3.00 m/s 2 )(0.37 m) v f = 3.2 m 2 /s m 2 /s 2 = 1.0 m 2 /s 2 v f = 1.0 m/s PTS: 1 DIF: IIIA OBJ: ANS: 111 m v i = 27.8 m/s v f = 0.0 m/s Δt = 8.00 s Δx = 1 (v + v )Δt = 1 (27.8 m/s m/s)(8.00 s) = 111 m 2 i f 2 PTS: 1 DIF: IIIA OBJ: ANS: at least 0.20 m a = g = 9.81 m/s 2 Δt = 0.20 s v i = 0.0 m/s Δx = v i Δt a(δt) 2 Δx = (0 m/s)(0.20 s) ( 9.81 m/s 2 )(0.20 s) 2 = 0.20 m PTS: 1 DIF: IIIA OBJ:

25 45. ANS: 44 m a = g = 9.81 m/s 2 Δt = 2.0 s v i = 12 m/s Δx = v i Δt a(δt) 2 Δx = ( 12 m/s)(2.0 s) ( 9.81 m/s 2 )(2.0 s) 2 = 44 m height of cliff = 44 m PTS: 1 DIF: IIIA OBJ: ANS: 19.6 m a = g = 9.81 m/s 2 v i = 24.5 m/s Δt = 1.00 s Δx = v i Δt a(δt) 2 Δx = (24.5 m/s)(1.00 s) ( 9.81 m/s 2 )(1.00 s) 2 = 19.6 m PTS: 1 DIF: IIIA OBJ: ANS: 0.00 m/s v 1 = 0.25 m/s east v 2 = 0.25 m/s west v R = v 1 v 2 = 0.25 m/s 0.25 m/s = 0.00 m/s PTS: 1 DIF: IIIA OBJ:

26 48. ANS: 13.0 blocks Students should use graphical techniques. Their answers can be checked using the techniques presented in Section 2. d = (12.0 blocks) 2 + (5.0 blocks) 2 = 13.0 blocks PTS: 1 DIF: IIIA OBJ: ANS: 12.2 m Students should use graphical techniques. Their answers can be checked using the techniques presented in Section 2. d = (12.0 m) 2 + (2.5 m) 2 = 12.2 m PTS: 1 DIF: IIIA OBJ: ANS: 2 3 v plane vplane = 120 km/h west = 120 km/h vwind = 40 km/h east = +40 km/h v R = v plane + v wind = 120 km/h + (40 km/h) = 80 km/h v R = 80 km/h v plane 120 km/h = 2 3 v R = 2 3 v plane PTS: 1 DIF: IIIA OBJ:

27 51. ANS: 62 steps Students should use graphical techniques. Their answers can be checked using the techniques presented in Section 2. d = (28 steps) 2 + (55 steps) 2 = 62 steps PTS: 1 DIF: IIIA OBJ: ANS: 43 m Δx 1 = m Δy 1 = 15 m Δx 2 = m Δx tot = Δx 1 + Δx 2 = ( m) + ( m) = m Δy tot = Δy 1 = 15 m d 2 = (Δx tot ) 2 + (Δy tot ) 2 d = (Δx tot ) 2 + (Δy tot ) 2 = ( m) 2 + ( m) 2 = m PTS: 1 DIF: IIIA OBJ: ANS: 92 m d = 120 m, θ = 40.0 d x = dcosθ = (120 m)(cos 40.0 ) = 92 m PTS: 1 DIF: IIIA OBJ:

28 54. ANS: 55 m d = 110 m θ = 30.0 d y = dsinθ = (110 m)(sin30.0 ) = 55 m PTS: 1 DIF: IIIA OBJ: ANS: 27 km/h north vpg = velocity of plane to ground = 145 km/h south vpa = velocity of plane to air = 172 km/h south v pg = v pa + v ag v ag = v pg v pa v ag = 145 km/h 172 km/h = 27 km/h v ag = 27 km/h north PTS: 1 DIF: IIIA OBJ: ANS: 27 N, to the right F 1 = 102 N, to the right F 2 = 75 N, to the left F net = F 1 + F 2 F net = F 1 F 2 = 102 N 75 N = 27 N F net = 27 N, to the right PTS: 1 DIF: IIIA OBJ:

29 57. ANS: 19 N Fx = 12 N, east Fy = 15 N, north F net = F x 2 + F y 2 = (12 N) 2 + (15 N) 2 = 19 N PTS: 1 DIF: IIIA OBJ: ANS: 269 N, downward Fballoon,y = 634 N, upward Fg = 365 N, downward ΣF y = F balloon, y F g F applied, y = 0 F applied, y = F balloon, y F g = 634 N 365 N = 269 N F applied, y = 269 N,downward PTS: 1 DIF: IIIA OBJ: ANS: 16 N m = 32 kg ax = 0.50 m/s 2 ΣF x = ma x = (32 kg)(0.50 m/s 2 ) = 16 N PTS: 1 DIF: IIIA OBJ:

30 60. ANS: 1.3 m/s 2, upward F applied, y = 277 N F g = 245 N m = 25 kg ΣF y = F applied, y F g = ma a = F applied, y F g m = a = 1.3 m/s 2, upward 277 N 245 N 25 kg = 1.3 m/s 2 PTS: 1 DIF: IIIA OBJ: ANS: 10.4 N m = 1.10 kg θ = 15.0 g = 9.81 m/s 2 F net, y = ΣF y = F n F g, y = 0 F n = F g, y = F g cosθ = mgcosθ F n = (1.10 kg)(9.81 m/s 2 )(cos15.0 ) = 10.4 N PTS: 1 DIF: IIIA OBJ:

31 62. ANS: 14 N, upward F g, 1 = 5 N F g, 2 = 9 N F g, 3 = 16 N F net, y = ΣF y = F n F g, 1 F g, 2 = 0 F n = F g, 1 + F g, 2 = 5 N + 9 N = 14 N Fn = 14 N, upward PTS: 1 DIF: IIIA OBJ: ANS: 0.22 F g = (6)(1.0 N) = 6.0 N F applied = 1.3 N F net, y = F n F g = 0 F n = F g F net, x = F applied F f = 0 F applied = F f µ k = F f F n = F applied F g = 1.3 N 6.0 N = 0.22 PTS: 1 DIF: IIIA OBJ:

32 64. ANS: 2.8 N m = 0.70 kg µ k = 0.41 g = 9.81 m/s 2 F net, y = F n F g = 0 F n = F g F net, x = F applied F f = 0 F applied = F f F f = µ k F n = µ k F g = µ k mg = ( 0.41)(0.70 kg)(9.81 m/s 2 ) = 2.8 N F applied = F f = 2.8 N PTS: 1 DIF: IIIA OBJ: ANS: 215 J F = 43.0 N d = 5.00 m W = Fd = ( 43.0 N) ( 5.00 m) = 215 J PTS: 1 DIF: IIIA OBJ:

33 66. ANS: J m = 88 kg h = 3.7 m g = 9.81 m/s 2 PE = mgh = 88 kgˆ 9.81 m/s 2 ˆ ( 3.7 m) = J PTS: 1 DIF: IIIA OBJ: ANS: J m = 80.0 kg h = 8848 m g = 9.81 m/s 2 PE = mgh = 80.0 kgˆ 9.81 m/s 2 ˆ ( 8848 m) = J PTS: 1 DIF: IIIA OBJ: ANS: J k = 275 N/m x = 3.25 cm = m PE = 1 2 kx2 = 1 2 ( 275 N/m) ˆ m = J PTS: 1 DIF: IIIA OBJ:

34 69. ANS: 0.54 m/s h = 1.5 cm = m g = 9.81 m/s 2 ME i = ME f mgh i = 1 mv 2 2 f v f = 2gh = ( 2) 9.81 m/s 2 ˆ m ˆ = 0.54 m/s PTS: 1 DIF: IIIA OBJ: ANS: 2.5 kw m = 250 kg d = 2.0 m Δt = 2.0 s g = 9.81 m/s 2 P = W Δt = Fd Δt = mgd Δt = 250 kg ˆ 9.81 m/s s ˆ ( 2.0 m) = W = 2.5 kw PTS: 1 DIF: IIIA OBJ: