Physics Chapter 3 Homework

1. As you read this in your chair, how fast are you moving relative to the chair? Relative to the Sun? Relative to my chair, my speed is 0. To the Sun around 107,000 km/hr. 2. What two units of measurement are necessary for describing speed? Distance traveled and how much time it took to go that distance. 3. What kind of speed is registered by an automobile speedometer: average speed or instantaneous speed? Instantaneous speed 4. What is the average speed in kilometers per hour of a horse that gallops a distance of 15 km in a time of 30 min? Around 30 km per hour 5. How far does a horse travel if it gallops at an average speed of 25 km/h for 30 min? I believe 12.5 kilometers 6. What is the main difference between speed and velocity? Speed is measured as scalar. And velocity is like a vector. 7. If a car moves with a constant velocity, does it also move with a constant speed? Yes, the car is moving at a constant velocity and a constant speed in a straight line. 8. If a car is moving at 90 km/h and it rounds a corner, also at 90 km/h, does it maintain a constant speed? A constant velocity? Defend your answers. Yes, but because the car changes direction the velocity changes too. 9. What is the acceleration of a car moving along a straight road that increases its speed from 0 to 100 km/h in 10 s? 10 km divided by hours multiplied by seconds 10. What is the acceleration of a car that maintains a constant velocity of 100 km/h for 10 s? (Why do some of your classmates who correctly answer the preceding question get this question wrong?) The cars acceleration is zero and velocity doesn’t change. 11. When are you most aware of your motion in a moving vehicle: when it is moving steadily in a straight line or when it is accelerating? If you were in a car that moved with absolutely constant velocity (no bumps at all), would you be aware of motion? When your car accelerates, but if your car could move at a constant velocity then you could not ever feel it moving. 12. Acceleration is generally defined as the time rate of change of velocity. When can it be defined as the time rate of change of speed? It would be change of velocity when the direction changes. 13. What did Galileo discover about the amount of speed a ball gained each second when rolling down an inclined plane? What did this say about the ball’s acceleration? He discovered that the speed increases in a straight line. 14. What relationship did Galileo discover about a ball’s acceleration and the steepness of an incline? What acceleration occurs when the plane is vertical? On a vertical plane, the balls momentum moves it less than a sloped plane. 15. What exactly is meant by a “freely falling” object? It is defined as an object that is free of any forces acting upon it. 16. What is the gain in speed per second for a freely falling object? 9.8 m/s 17. What is the speed acquired by a freely falling object 5 s after being dropped from a rest position? What is the speed 6 s after? 50 and 60 m/s 18. The acceleration of free fall is about 10 m/s2 . Why does the seconds unit appear twice? It occurs twice because 1 time is for velocity and the 2 time is when you divide the change in velocity to find the acceleration rate 19. When an object is thrown upward, how much speed does it lose each second (ignoring air resistance)? Without the air slowing it down, 10 m/s 20. What relationship between distance traveled and time did Galileo discover for freely falling objects released from rest? Galileo found that the distance traveled by a uniformly accelerating object that starts from rest 21. What is the distance fallen for a freely falling object 1 s after being dropped from a rest position? What is the distance for a 4-s drop? The object starting at rest falls at 5m per second, past 4 seconds it will fall 80m 22. What is the effect of air resistance on the acceleration of falling objects? It slows the object down significantly. 23. Consider these measurements: 10 m, 10 m/s, and 10 m/s2 . Which is a measure of speed, which of distance, and which of acceleration? 10 m/s means speed, 10 m is referring to distance, and 10m/s2 is the acceleration. 24. What is the speed over the ground of an airplane flying at 100 km/h relative to the air caught in a 100-km/h right-angle crosswind? The ground speed is 141 km/h. 28. Stand flat-footed next to a wall. Make a mark on the wall at the highest point you can reach. Then jump vertically and mark this highest point. The distance between the two marks is your vertical jumping distance. Use these data to calculate your personal hang time. My average vertical jump is seventeen inches. 30. Calculate your average walking speed when you step 1.0 m in 0.5 s. 2.0 m/s 32. Show that the acceleration of a hamster is 5 m/s2 when it increases its velocity from rest to 10 m/s in 2 s. 5.0 m/s 34. Show that a freely falling rock drops a distance of 45 m when it falls from rest for 3 s. Distance= 1/2gt squared = ½ * 10 m/s squared * 3seconds =45m 36. A ball is tossed with enough speed straight up so that it is in the air several seconds. (a) What is the velocity of the ball when it reaches its highest point? (b) What is its velocity 1 s before it reaches its highest point? (c) What is the change in its velocity during this 1-s interval? (d) What is its velocity 1 s after it reaches its highest point? (e) What is the change in velocity during this 1-s interval? (f) What is the change in velocity during the 2-s interval? (Careful!) (g) What is the acceleration of the ball during any of these time intervals and at the moment the ball has zero velocity? The velocity of the ball at its highest point is zero, for just a moment. One second before reaching the top, the ball has a velocity of 10 m/s. The change in its velocity is 0-10 m/s = -10 m/s for this 1-second interval (or for any other 1-second-long interval during freefall). One second after reaching the top, its velocity is -10 m/s, which equal in magnitude but directed opposite to its velocity 1 second before reached the highest point. The change in velocity is -10 m/s - 0 m/s = -10 m/s for this 1-second interval (or for any other 1-second-long interval during freefall). For the 2-second interval, the change in velocity is -10 m/s - 10 m/s = -20 m/s. A common mistake is to think that the change is zero, but there is a nonzero change in velocity because the ball's direction has changed. The acceleration of the ball is −10 m/s2 at all times. 38. A car takes 10 s to go from v = 0 m/s to v = 25 m/s at constant acceleration. If you wish to find the distance traveled using the equation d = 1/2at2 , what value should you use for a? 2.5 m/s squared 40. A dart leaves the barrel of a blowgun at a speed v. The length of the blowgun barrel is L. Assume that the acceleration of the dart in the barrel is uniform. a. Show that the dart moves inside the barrel for a time of 2L/v. b. If the dart’s exit speed is 15.0 m/s and the length of the blowgun is 1.4 m, show that the time the dart is in the barrel is 0.19 s 0.19s 42. A track is made from a piece of channel iron as shown. A ball released at the left end of the track continues past the various points. Rank the speeds of the ball at points A, B, C, and D, from fastest to slowest. (Watch for tie scores.) C, B= D, A 44. Three balls of different masses are thrown straight upward with initial speeds as indicated. a. From fastest to slowest, rank the speeds of the balls 1 s after being thrown. b. From greatest to least, rank the accelerations of the balls 1 s after being thrown. (Or are the accelerations the same?) A.) C,B,A B.) A=B=C 46. Here we see top views of three motorboats crossing a river. All have the same speed relative to the water, and all experience the same river flow. Construct resultant vectors showing the speed and direction of each boat. Rank the boats from most to least for a. the time to reach the opposite shore. b. the fastest ride. B ,A, C and C, B, A 48. Jo, with a reaction time of 0.2 second, rides her bike at a speed of 6.0 m/s. She encounters an emergency situation and “immediately” applies her brakes. How far does Jo travel before she actually applies the brakes? 1.2m 50. Suzie Surefoot can paddle a canoe in still water at 8 km/h. How successful will she be canoeing upstream in a river that flows at 8 km/h? She will not be able to move the canoe. 52. One airplane travels due north at 300 km/h while another travels due south at 300 km/h. Are their speeds the same? Are their velocities the same? Explain. The airplane speeds are the exact same, but the velocities are different. 54. You’re traveling in a car at some specified speed limit. You see a car moving at the same speed coming toward you. How fast is the car approaching you, compared with the speed limit? The other car is doing twice as much as the speed limit. 56. Jacob says acceleration is how fast you go. Emily says acceleration is how fast you get fast. They look to you for confirmation. Who’s correct? Emily is more correct but still a little wrong. 58. What is the acceleration of a car that moves at a steady velocity of 100 km/h for 100 s? Explain your answer. The acceleration would end up being zero. Because the steady velocity it does not affect the acceleration or take off rate. 60. Galileo experimented with balls rolling on inclined planes of various angles. What is the range of accelerations from angles 0° to 90° (from what acceleration to what)? From zero to 10m/s squared 62. Suppose that the freely falling object in the preceding exercise were also equipped with an odometer. Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds? The odometer reading means the distance fallen was completed in 1 second 64. If air resistance can be ignored, how does the acceleration of a ball that has been tossed straight upward compare with its acceleration if simply dropped? The force it was thrown with effects how fast it falls because the acceleration was more initially. 66. Boy Bob stands at the edge of a cliff (as in Figure 3.8) and throws a ball nearly straight up at a certain speed and another ball nearly straight down with the same initial speed. If air resistance is negligible, which ball will have the greater speed when it strikes the ground below? The balls will hit the ground at the same time. 68. While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20? The ball would have rolled 4 cubits 70. Extend Tables 3.2 and 3.3 to include times of fall of 6 to 10 s, assuming no air resistance. Time of fall (seconds) Distance fallen (m) 6s 180m 7s 245m 8s 320m 9s 405m 10s 500m 72. As speed increases for an object in free fall, does acceleration increase also? No 74. Why would a person’s hang time be considerably greater on the Moon than on Earth? Lack of serious gravity, it goes to about 1/6 of on earth 76. Vertically falling rain makes slanted streaks on the side windows of a moving automobile. If the streaks make an angle of 45°, how does the speed of the automobile compare with the speed of the falling rain? Both speeds are the exact same. 78. Make up a multiple-choice question that would check a classmate’s understanding of the distinction between velocity and acceleration. If a jogger was running at a speed of 4 miles an hour, and they ran for 2 hour, accelerating every hour what would their average speed be? 80. Can an object reverse its direction of travel while maintaining a constant acceleration? If so, cite an example to your classmates. If not, provide an explanation. Yes 82. Correct your friend who says, “The dragster rounded the curve at a constant velocity of 100 km/h.” Constant speed not constant velocity. 84. Cite an instance in which your speed could be zero while your acceleration is nonzero. A ball thrown straight upward has zero speed at the very top of its flight, but acceleration there has a magnitude of 10ms2 directed downward. 86. (a) Can an object be moving when its acceleration is zero? If so, give an example. (b) Can an object be accelerating when its speed is zero? If so, give an example. a. Yes. For example, an asteroid moving in deep space at constant velocity. b. Yes. For example, a vertically thrown projectile at the top of its flight path. 88. On which of these hills does the ball roll down with increasing speed and decreasing acceleration along the path? (Use this example if you wish to explain to someone the difference between speed and acceleration.) The middle one I believe 90. Be picky and correct your friend who says, “In free fall, air resistance is more effective in slowing a feather than a coin.” Free fall is defined as falling with no air resistance. 92. In the preceding exercise, can you think of a reason why the acceleration of the object thrown downward through the air might be appreciably less than 10 m/s2 ? Discuss your reason with your classmates. Air resistance lowers magnitude, so the object gains less speed. 94. Madison tosses a ball straight upward. Anthony drops a ball. Your discussion partner says both balls undergo the same acceleration. What is your response? Your partner is correct; both balls undergo the same acceleration in the absence of air resistance. 96. Refer to the pair of tracks in the preceding exercise. (a) On which track is the average speed greater? (b) Why are the speeds of the balls at the ends of the tracks the same a. Average speed is distance divided by time, and the distances are equal. The ball on track B finishes first, so it has the higher average speed. b. The ball is moving equally fast at the ends of tracks A and B because the ball has dropped an equal distance from the starting point. In other words, the speed gained on the additional down ramp for B is lost when it climbs the final up ramp. 98. If raindrops fall vertically at a speed of 3 m/s and you are running horizontally at 4 m/s, convince your classmates that the drops will hit your face at a speed of 5 m/s. 5m/s 100. In this chapter, we studied idealized cases of balls rolling down smooth planes and objects falling with no air resistance. Suppose a classmate complains that all this attention focused on idealized cases is worthless because idealized cases simply don’t occur in the everyday world. How would you respond to this complaint? How do you suppose the author of this book would respond? We walk before we run, so you must complete other tasks before you complain. The author would respond by saying he disagrees.