Quest Chapter 09. Eliminate the obviously wrong answers. Consider what is changing: speed, velocity, some part of velocity? Choose carefully.

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1 1 A dragster maintains a speedometer reading of 100 km/h and passes through a curve with a constant radius. Which statement is true? 1. The dragster rounded the curve at a changing speed of 100 km/h. 2. The dragster rounded the curve at a changing velocity of 100 km/h. 3. The dragster moved along a straight line at a constant velocity of 100 km/h. 4. The dragster rounded the curve at a constant velocity of 100 km/h. 5. All are wrong. 2 Why is the linear speed greater for a horse on the outside of a merry-go-round than for a horse closer to the center? 1. The horse on the outside has longer legs. 2. The outside horse moves easier. 3. The tangential speed of the horse is directly proportional to the distance from the center. 4. The horse on the outside is larger. 5. None of these 6. The horse on the outside feels less force from the merry-go-round. Quest Chapter 09 Eliminate the obviously wrong answers. Consider what is changing: speed, velocity, some part of velocity? Choose carefully. Eliminate the obviously wrong answers. In terms of circular motion, what is the direction of something that has linear speed? In circular motion, what determines linear speed?

2 3 A large wheel is coupled to a wheel with half the diameter as shown. How does the rotational speed of the smaller wheel compare with that of the larger wheel? How do the tangential speeds at the rims compare (assuming the belt doesn t slip)? 1. The smaller wheel has half the rotational speed and half the tangential speed as the larger wheel. 2. The smaller wheel has twice the rotational speed and the same tangential speed as the larger wheel. 3. The smaller wheel has four times the rotational speed and the same tangential speed as the larger wheel. 4. The smaller wheel has twice the rotational speed and twice the tangential speed as the larger wheel. 4 A young boy swings a yo-yo horizontally above his head so that the yo-yo has a centripetal acceleration of 290 m/s 2. If the yo-yo s string is 0.98 m long, what is the yo-yo s tangential speed? 5 As viewed by a bystander, a rider in a barrel of fun at a carnival finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her? Coupled means as one turns the other turns as if they were touching. How many times does the small turn when the big wheel makes one revolution? (You may need to compare their circumferences.) So, when the rotational speed of the small wheel has to be what compared to the big wheel? Now, compare the linear speeds now that you know the relative rotational speeds. Remember, the equation for centripetal acceleration is: a=v 2 /r Substitute and solve. Draw a simple diagram so can label it. Label the force you know, Weight. What keeps her from sliding down? (don t think of the rotation yet) Label it. What causes that force? Think back to our discussion on Newton s 3 rd Law. Label it. Pick the best answer.

3 6 When you are in the front passenger seat of a car turning to the left, you may find yourself pressed against the right-side door. What concept(s) explain(s) why you press against the door and why the door presses on you? 1. Newton s first and third laws 2. centrifugal force and Newton s first law 3. centrifugal force and Newton s second law 4. just a centrifugal force Draw a simple diagram. Label the force that makes you turn left. On what does that force act? Is that the only force? What happens because of the first force? On what does that act? 7 The sketch shows a conical pendulum. The ball swings in a circular path because of the string attached at the top. The tension T in the string and weight W of the ball are shown by vectors. A parallelogram created with these vectors shows that their resultant F lies in the plane of the circle. What is the name of this resultant force F? 1. centrifugal force 2. angular force 3. centripetal force 4. frictional force 8 Two identical objects go around circles of identical diameter, but one object goes around the circle twice as fast as the other. The centripetal force required to keep the faster object on the circular path is 1. one fourth as much force as required to keep the slower object on the path. 2. half as much force as required to keep the slower object on the path. 3. the same force required to keep the slower object on the path. 4. twice as much force as required to keep the slower object on the path. 5. four times as much force as required to keep the slower object on the path. Eliminate obviously wrong answers. Look at the diagram. Where is the resultant vector pointed? What do we call that force? Use the equation for centripetal acceleration: F = mv 2 /r What happens to the force is the speed is doubled?

4 9 You are a passenger in a car and not wearing your seat belt. Without increasing or decreasing its speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is the correct analysis of the situation? 1. Neither of these 2. Starting at the time of collision, the door exerts a leftward force on you. 3. Both of these 4. Before and after the collision, there is rightward force pushing you into the door. 10 The sketch shows a coin at the edge of a turntable. The weight of the coin is shown by the vector W. Two other forces act on the coin, the normal force and a force of friction that prevents it from sliding off the edge. Draw force vectors for both of these. What forces act on you? What is the source of that force? Ignore the N label in the answer choices. It is only confusing. Where should the vectors point? 11 The value of g at the Earth s surface is about 10 m/s 2. How would this value change if the Earth rotated faster about its axis? 1. It depends on the latitude. 2. no change 3. decrease 4. increase 12 A ball rolls around a circular wall, as shown in the figure below. The wall ends at point X. When the ball gets to X, which path does the ball follow? 1. Path E 2. Path A 3. Path D 4. Path C 5. Path B Which answer has the vectors pointing in those directions? What would be reaction to something on the surface of the Earth if the Earth were to increase its rotational speed? What would that do to the force of gravity? When the ball reaches point X, what no longer acts on it? What is its direction at that point? Pick the correct path.

5 13 If you partially fill a bucket with water and swing it fast enough in a circle over your head, the water will stay in the bucket even when it is upside down. Which statement is not true? 1. The bucket has a downward force on the water in it. 2. The acceleration of the water is greater than g. 3. The acceleration of the water is less than g. 14 Consider a too-small space habitat that consists of a rotating cylinder of radius 4 m. If a man standing inside is 2 m tall and his feet are at 1 g, what is the g force at the elevation of his head? (Do you see why projections call for large habitats?) 1. 4 g 2. 2 g g g You are considering what is happening with the bucket when it is over your head. Answers 2 and 3 contradict each other. What must the acceleration of the water be in order for it to stay in the bucket? Use the centripetal force equation for this: F = mrω 2. Except F=g (g=weight) when r = 4m. Assume the m = 1kg. Find ω. This will be constant for any value of r. Now, reuse the equation, F = mrω 2. using r = 2 and the newly found ω. Solve for F.

6 15 An engineer is constructing a space habitat out of a cylinder. In order to create artificial gravity, the engineer decides to induce a rotation in the habitat. If the variation in g between one s head and feet is to be less than g/86, then compared to one s height, what should be the minimum radius of the space habitat? (Assume that a person s height is 2 m.) You are designing a rotating space station. It rotates to simulate gravity. If the radius is too small, the astronauts will not adjust to the environment. So, the force felt at the head must be almost the same as the force felt at the feet. Use the centripetal force equation F = mrω 2 twice. Use g for the force in the first equation and (1-1/86)g for the force in the second equation. Use r in the first equation and (r-2) in the second equation. Assume the m = 1 kg. (Mass drops out.) Solve for the rotational speed, ω, for it is the same for both equations. Set the equations equal to each other and solve for r.

7 16 The occupant inside a rotating space habitat of the future feels that she is being pulled by artificial gravity against the outer wall of the habitat (which becomes the floor). Which statement is false? 1. The floor intercepts her path and presses against her feet. 2. The floor provides the centripetal force to keep her moving in a circular path. 3. At every moment her tendency is to move in a straight-line path. 4. Centrifugal force causes her to move in a circular path. 17 (part 1 of 2) A hawk flies in a horizontal arc of radius 17.9 m at a constant speed of 3.3 m/s. Find its centripetal acceleration. Answer in units of m/s 2 18 (part 2 of 2) It continues to fly along the same horizontal arc but increases its speed at the rate of 0.65 m/s 2. Find the magnitude of acceleration under these new conditions. Answer in units of m/s 2 You are looking for a FALSE statement. Recheck your notes. Use: a centripetal = v 2 /r Is r changing? No. Is a centripetal changing? No. But, v tangential is changing. Since centripetal and tangential directions are perpendicular, you use the Pythagorean Theorem to solve this one.

8 19 (part 1 of 2) An airplane is flying in a horizontal circle at a speed of 121 m/s. The 85.0 kg pilot does not want the centripetal acceleration to exceed 7.15 times free-fall acceleration. a) Find the minimum radius of the plane s path. Answer in units of m Free-fall acceleration is 1 g (or 1 times a g ). Use a centripetal = v 2 /r. Set a centripetal = the correct multiple of a g in your problem. (In this example, that would be 7.15 a g.) Set v = the speed in your problem. (In this example, that would be 121 m/s.) 20 (part 2 of 2) 10.0 points b) At this radius, what is the magnitude of the net force that maintains circular motion exerted on the pilot by the seat belts, the friction against the seat, and so forth? Answer in units of N 21 (part 1 of 2) A 69.4 kg ice skater is moving at 8.99 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius m around the pole. The acceleration of gravity is 9.8 m/s 2. Find the force exerted by the rope on her arms. Answer in units of kn 22 (part 2 of 2) Find the ratio of this tension to her weight. Solve for r in the equation. You have an acceleration. You have a mass (In this example, the mass is 85 kg). Use the second law of motion: F=ma to find the force. You have mass (69.4 kg). You have velocity (8.99 m/s). You have radius (0.872 m). Find F: F centripetal = mv 2 /r Be mindful of the units (kn) for the answer. Ratio? First over Last. Make sure to calculate her weight.

9 23 A bucket full of water is rotated in a vertical circle of radius m (the approximate length of a person s arm). What must be the minimum speed of the pail at the top of the circle if no water is to spill out? Answer in units of m/s 24 A dancer moves around a path like the one shown in the figure below with a constant speed. Which of the following best represents the magnitude of the dancer s acceleration as a function of time t during one trip around the path, beginning at point P? At the top of the circle, the a centripetal must equal the magnitude of a g. Use a g = 9.81 m/s 2. Solve for v in a centripetal = v 2 /r. In each section of the path, between the points P to Q, Q to R, R to S, and S to Q, what is the acceleration of the dancer. Is the change from one acceleration to another gradual or sudden? Is each acceleration changing or is each one constant during the interval?