PHYSICS 1050 Mid-term Test 1 University of Wyoming 15 February 2005

Transcription

1 Name: (4 points) ANSWER KEY PHYSICS 1050 Mid-term Test 1 University of Wyoming 15 February 2005 This test is open-note and open-book. This means that any reference material is permitted during the test. Calculators also are permitted. However, no collaboration, consultation, or communication is allowed by any means, including but not limited to verbal, written, or electronic methods. If you have a question about the test, please raise your hand. If that does not get the administrator s attention, throw something at him. He may try to climb across the desks to hear your question, but he will probably resort to asking you to shout across the room, since once everyone is in their seats, it is really hard to get in or out. Please do not open this test booklet until everyone has received a booklet and the test administrator has indicated for you to begin. While you are waiting, make sure that your name is written at the top of this page. Not only will that get you four easy points, it will save you the trouble of trying to convince the instructor that some high-scoring test with no name on it is really yours. Conversion Factors: 12 in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi Physical Constants: 2.54 in = 1 cm in = 1 m 1 lb = 4.5 N 1 day = 24 h 1 h = 60 min 1 min = 60 s Universal gravitational constant gravitational acceleration at earth s G = Nm 2 kg 2 surface: g = 9.8 m/s 2 = 9.8 N/kg Metric Prefixes: pico: nano: 10-9 micro; 10-6 milli: 10-3 centi: 10-2 kilo: 10 3 mega: 10 6 giga: 10 9 tera: A

2 Multiple choice 20 questions, 3 points each. Please circle the most correct answer from the choices given. 1. Before the Revolution, the French used a unit of length called the toise. The toise was longer than the meter. If a mountain is exactly 2000 toises high, its height in meters is a. exactly 2000 meters b. less than 2000 meters c. more than 2000 meters 2. The speed limit on Willett Drive by the Arena is 20 miles per hour. How can this be converted into the SI units of meters per second? 60 min a. 20 mi h 60s 5280 ft 12 in in = wrong initial units h min mi ft m b. 20 mi 5280 ft 12 in in 60 min 60s h mi ft m h min = in, h don t cancel c. 20 mi h h min 5280 ft 12 in m 60 min 60 s mi ft in = d. 20 mi 5280 ft 12 in m 3600 s = h don t cancel h mi ft in h 3. Which of the four vectors illustrated has the largest magnitude? 4. The proper way to add vectors A r and B r to obtain the vector sum A r + B r is shown in which diagram below? A page 2 of 12

3 5. The graph to the right shows the progress made by a beetle moving along a straight line. If the beetle keeps moving at the same speed, at what time will it reach the 10-cm mark? a. 4 seconds b. 10 seconds c. 20 seconds d. 25 seconds 6. When a car accelerates uniformly from rest, which quantities increase with time? a. acceleration and velocity b. velocity only c. acceleration and distance traveled d. velocity and distance traveled 7. A car driving in the fog rear-ends a stopped semi-trailer. The car stops instantly, and the driver, not wearing his seat belt, impacts the steering wheel. The impact brings him to a stop in s. If the driver s air bag had deployed, he would have come to a stop in s. Which of the following statements is true? a. The driver s change in speed is less with the airbag than without. b. The force on the driver with the airbag is greater than if the airbag were not there. c. The force on the driver with the airbag is less than if the airbag were not there. d. The air bag reduces the driver s kinetic energy more than the steering wheel alone does. No: goes from 0.5 mv 2 to 0 in both cases. No: v is the same 8. Two balls of the same mass and moving with the same velocity collide with a wall. Ball A, made of soft clay, sticks to the wall. Ball B, made of rubber, bounces back from the wall. Which ball experiences the largest change in momentum before and after the collision? a. Ball A. p Ai = mv; p Af = m(0)= 0; p A = mv 0 = mv b. Ball B. p Bi = mv; p Bf = m( v)= mv; p B = mv ( mv) = 2mv c. Both have the same change in momentum. d. You can t tell because you don t know the time t of the collisions. F = v/ t t is different A page 3 of 12

4 9. You are a mechanical engineer hired to design the loop-the-loop roller coaster for a new amusement park. What do you need to consider in your design to keep riders from falling out of the coaster at the top of the loop? a. The inward acceleration of the coaster at the top of the loop must be more than g. b. The speed of the coaster must be greater than terminal velocity of free fall. c. Do not allow riders who are too heavy on the coaster. d. The force holding passengers up must exceed the force pulling them down. 10. There is a location between the Earth and the moon, called the Lagrange Point, where the gravitational forces from the Earth and the moon cancel. An object placed exactly at the Lagrange Point will not accelerate toward either the moon or the earth. Since the Earth is more massive than the moon, the Lagrange point a. is closer to the Moon than to the Earth. b. is exactly midway between the moon and Earth. c. is closer to the earth than to the moon. d. is at a distance that depends on the phase of the moon. 11. A central particle is surrounded by two circular rings of particles, as shown to the right. All the particles have mass m. What is the direction of the net gravitational force on the central particle due to the particles in the rings? a. toward the top of the page (up) b. to the right c. toward the bottom of the page (down) d. to the left F = Gm 1m 1 r 12 2 Need to get closer to the moon to equal the pull of gravity from the larger Earth A page 4 of 12

5 12. The diagram to the right shows a person holding a ball standing at three different places on Earth. If the person drops the ball, gravity will make it fall. Which of the diagrams below best shows the direction the dropped ball will fall at the three different positions? 13. My dog weighs 43 pounds. That means that the Earth exerts a gravitational force of 43 pounds on my dog. The gravitational force my dog exerts on the earth is a. 43 pounds, because of Newton s third law. b. Less than 43 pounds, because my dog s gravitational field is much less than the Earth s. c. Zero, because a dog is too small to have gravity. d. More than 43 pounds, but the Earth is so massive it doesn t accelerate. 14. The mass of the planet Mars is about 1/10 the mass of Earth, and its radius is about 1/2 the radius of earth. The weight of the Mars probe Odyssey when it is on the surface of Mars is a. about 1/10 its weight on Earth. b. more than 1/10 its weight on Earth. c. less than 1/10 its weight on Earth. Mars s radius is less than Earth s, so at the surface you are closer to the center. if Odyssey were a distance equal to the radius of the Earth from the center of Mars, its weight would be 1/10 its weight on Earth. Since it is closer, its weight is more than that. A page 5 of 12

6 15. The diagram above on the left shows a ball on the end of a string being whirled in a circle. The diagram on the right shows the whirling ball as viewed from above. After several whirls, the string is released when the ball is at Q. Which of these diagrams shows the direction in which the ball will fly, as viewed from above, the instant the string is released? 16. You are riding in the right side of a car when the driver makes a hard left turn. You feel yourself pressing against the door because a. you are accelerating outward as the car turns in a curved path. b. the car tilts to the right, so gravity pushes you onto the door. c. the car is accelerating leftward as it turns, pushing into you. d. you are pushing outward on the door, so the door pushes back with an equal and opposite force. A page 6 of 12

7 17. Alex is has a flat tire. The guy at the garage, as usual, over-tightened the nuts when he mounted the tire, so Alex is having trouble loosening them. Which direction should Alex push on the handle of the lug wrench to get the maximum torque about the nut? a. straight inward b. obliquely outward c. perpendicular to the handle d. obliquely inward 18. The diagram below shows the positions at 1-second intervals of a ball that is thrown upward from (0, 0)at an angle. 100 Height (m) Distance (m) Between the start of the ball s trajectory at (0, 0) and the end at (0, 240 m), a. the ball s kinetic energy is constant. That s total energy. b. the ball s kinetic energy initially decreases, then passes through zero and increases again. Only if the ball has no horizontal speed. c. the ball s kinetic energy initially decreases, then reaches a minimum value and increases again. d. the ball s kinetic energy initially increases, then reaches a maximum value and decreases again. That s potential energy. A page 7 of 12

8 19. Until he was in his seventies, Henri LaMothe excited circus audiences by bellyflopping from a height of 12 m into 30 cm of water. How can you find what his kinetic energy KE was when he hit the water? a. Estimate his mass m, then use KE =1 2mv 2. b. Estimate his mass m, then use KE = work = mgh with h = 12 m. c. Estimate his falling power, then use P = w t w = P t to find the work needed. d. Solve the equation h = v 0 t +1 2a t ( ) 2 for v. 20. The SI unit for energy is the joule, but power companies usually bill by the kilowatt hour (kwh), which is the energy consumed by applying the power of 1000 watts for 1 hour. How can you find how many joules are equal to one kwh? a W 1 h 3600 s h c W 1 h 3600 s h J/s W =L b. 1 h 3600 s W 1000 W h J/s =L J/s W =L 1 kwh = 1000 W 1 h, not 1000 W / h or h / 1000 W. Short answer 5 questions, 4 points each s d W 1 h W s =L h J 21. The diagram below shows the positions at intervals of 0.05 s of two balls moving from left to right. Are either or both of these balls accelerated? Explain. Both are accelerated, which means that their velocities are not constant. If their velocities were constant, the spacing between intervals would be constant, and it is not. Ball A is accelerating to the right, and ball B is decelerating, or accelerating toward the left. A page 8 of 12

9 22. A skydiver jumps out of a perfectly good airplane. For a few seconds, she accelerates toward the ground, but eventually her velocity reaches a maximum value of terminal velocity, so that her falling speed does not change with time. a. Identify two forces that are acting on her body as she falls. gravity and air resistance b. In what directions are these two forces acting? gravity pulls downward and air resistance opposes the direction of her motion. c. What are the relative magnitudes of these two forces before and after she reaches terminal velocity? Before she reached terminal velocity, the pull of gravity was greater than air resistance, which is why she accelerated. After she reached terminal velocity, she was not accelerating, so the total force acting on her was zero. This means that the forces of gravity and air resistance, which were oppositely directed, had equal magnitudes. 23. A feather falls more slowly than a paperweight. Why? (Don t just identify the forces that are acting on each object; explain why their effects are different for the two different objects.) The motion of both objects is governed by their masses and the forces of gravity and air resistance acting on them. The force of air resistance is a greater fraction of the feather s weight than of the paperweight s weight. The force of air resistance thus more effectively acts against the force of the feather s weight than the paperweight s weight. A page 9 of 12

10 24. The diagram shows the locations at 1-second intervals of a ball thrown at 50 m/s at an angle of ~53 form horizontal. At each location, draw a vector showing the magnitude and direction of the ball s acceleration. (Since there is no scale of acceleration units on the graph, you only need to make the relative magnitudes at the different locations consistent with each other.) 100 The acceleration is due to the force of gravity, which acts only downward. Height (m) Distance (m) 25. Why is it harder to open a door when you push near the hinge than when you push on the opposite side, away from the hinge? When you push away from the hinge, you have a longer lever arm. Since the torque you are applying to the door about the hinge is the force of your push multiplied by the length of the lever arm, the torque is higher away from the hinge than close to it. A page 10 of 12

11 Calculation 4 questions, 4 points each. The following questions require numerical answers. Show your work, and include the units with your answers. 26. A single force of 40 N acts upon a 5-kg block. What is the magnitude of the acceleration of the block? (Don t forget the units!) F = ma, so a = F/m = (40 N)/(5 kg) = 8 (kg m/s 2 )/kg = 8 m/s A rifle fires a bullet with a mass of 5.0 g (0.005 kg). The bullet moves with a muzzle velocity of 1000 m/s after the rifle is fired. What is the momentum of the bullet after the rifle is fired? (Don t forget the units!) p = mv = (0.005 kg)(1000 m/s) = 5 kg m/s A page 11 of 12

12 28. A 100-kg mawg (half-man, half-dog) weighs 3000 N on the planet Druidia. What is the gravitational acceleration on Druidia? (Don t forget the units!) F = ma, so a = F/m = (3000 N)/(100 kg) = 30 N/kg = 30 m/s 2 This is a crushingly high gravity, about triple that of Earth. 29. A force of 50 N is applied to the end of a wrench handle that is 24 cm long. The force is applied in a direction perpendicular to the handle as in the diagram. What is the torque (both direction and magnitude, including units) applied to the nut by the wrench? = F r = (50 N)(0.24 m) = 12 Nm By the right-hand rule, the torque vector is directed into the plane of the paper, away from you. A page 12 of 12