Exam I solutions Name: Date: 1. Two cars are moving around a circular track at the same constant speed. If car 1 is at the inner edge of the track and car 2 is at the outer edge, then A) the acceleration of car 1 is less than the acceleration of car two. B) the accelerations of both cars are equal and greater than zero. C) the acceleration of car 1 is greater than the acceleration of car 2. D) the accelerations of both cars are zero. You know that centripetal acceleration is involved because it is circular motion. The formula is 2 v a c =. They have the same speed but car 1 has a smaller radius and that will mean greater r acceleration since r is in the denominator. The answer is C. 2. A single constant 10-pound force F 1 acts on a body, causing it to accelerate. Then, while F 1 continues to act, a second constant force F 2 is applied to the body, which comes to a momentary stop. The magnitude of F 2 is A) zero. B) a bit less than 10 pounds. C) exactly 10 pounds. D) larger than 10 pounds. E) not enough information to tell. If F 2 were equal or less than to F 1 the mass could not stop moving. At most, it would stop accelerating (if the two forces were oppositely directed and therefore cancelled.) Thus, it must be that the second force is larger than 10 pounds. The answer is D. 3. An auto moves 10 meters in the first second of travel, 10 more meters in the next second and 10 meters during the third second. The acceleration of the auto in m/s 2 is A) 3.33 B) 9.8 C) 30 D) 10 E) Zero. It is clear that the auto is moving at constant velocity since it constantly covers the same distance in one second (10 meters). Thus, the acceleration is zero. The answer is E. 4. A 10 pound iron ball and a 2 pound iron ball are dropped simultaneously from a height of 100 meters. Neglecting air resistance, which ball will reach the ground first? A) The 10 lb ball. B) The 2 lb ball. C) They will reach the ground at the same time. Gravity produces a force proportional to mass, so the acceleration does not depend on mass. It will be 9.81 m/s 2 for both, so they will hit the ground at the same time. Answer: C Page 1
5. Suppose an artificial satellite has been put into circular orbit about the Earth, at a distance from the center of the Earth equal to 1/4 the distance from the Earth's center to the Moon's center. In terms of the Moon's period T m, what will be the period of the satellite? A) 16T m. B) 8T m. C) T m. D) T m /8. E) T m /16. T T This involves Kepler s third law. = const. = If you cross multiply and take the square 3 3 R R root of both sides then you get : 3 3 3 T R 1 1 1 = = = =. T R 4 2 8 6. A ball is thrown across the street. During its flight, the ball's speed is lowest at A) The beginning of its flight. B) The end of its flight. C) The highest point of its flight. D) The speed is constant throughout the flight. For projectile motion the horizontal component of the velocity is a constant. The vertical component, however, has a constant negative acceleration due to gravity. The vertical component starts out positive, decreases to zero, and then becomes negative has the ball falls. 2 The total velocity is related to the components as the sides of a triange: v = vx + vy. Vx is a constant and Vy is a minimum in magnitude when it goes to zero at the highest point of the flight. Thus, the total speed is a minimum there. The answer is C. 7. Your mass is 50 kg. Suppose you are standing on a scale in an elevator, that is approaching a top floor and decreasing its speed at the rate of 2 m/s every second. What would be a reading on the scale? A) 600 N B) 500 N C) 400 N D) 100 N E) 0. Firstly you can see that the acceleration is -2m/s 2. Therefore the net force is -50kg*2m/s 2 = - 100N. There are two forces here. One is the force of gravity =-50kg*10m/s 2 =-500 N and the other is the force of the scale pushing upward on your feet (this is what the scale reading tells you). F net =F gravity +F scale. ; -100N=-500N+F scale. ; F scale =400N. Answer: C 8. An object undergoes circular motion. Which pair of quantities MUST change? A) the object's speed and acceleration. B) the object's velocity and acceleration. C) the object's mass and speed. D) all of the above. Circular motion can be at constant speed and mass, but both the acceleration and velocity are Page 2
vectors which point toward the center of the circle. As the object moves around the circle, the direction toward the center of the circle must change. Thus, both the objects velocity and acceleration must change. Answer B. 9. The power of an engine is a measure of A) its volume. B) its ability to outperform a horse. C) the rate at which it can perform work. D) the total amount of work it can perform. This is the definition of power: the rate at which work is being done. Answer C. 10. The tendency of an auto to maintain its velocity is called A) mass. B) inertia. C) momentum. D) speed. This is the definition of inertia. Answer B. 11. Work is not being done on an object unless the A) net force on the object is zero. B) object is being accelerated. C) speed is constant. D) object is moving. Work is force times displacement. The speed does not need to be a constant, but the object does need to move. Answer D. 12. A pendulum swings through 10 cycles in 5 seconds. The frequency of the pendulum is A) 10 Hz. B) 5 Hz. C) 2 Hz. D) 0.5 Hz. E) 0.1 Hz. Frequency is the number of cycles per second. f = 10/5 = 2 Hz. Answer C. 13. Two blocks of equal mass are connected by a string. The system is accelerated across a smooth horizontal surface by a force supplied by a rubber band connected to the leading block. The tension in the connecting string will be A) the same as the force pulling the leading block. B) less than the force pulling the leading block. C) greater than the force pulling the leading block. D) zero. This is directly from a homework problem. The rubber band must supply the force to accelerate both blocks, but the string supplies the force to accelerate the second block only. Answer B. Page 3
14. A bullet is fired horizontally aiming straight at the center of a target with an initial velocity of 1000m/s. The target is located 150 m from the rifle. How far below the center of the target will the bullet hit? A).1125m B) 11.25 m C) 1.5 m D) 0 m This is just slightly modified from the homework problem. First of all, the time it takes for the d 150m bullet to reach the target is t = = = 0.15sec. The whole time it is traveling it is falling. v 1000 m s 1 2 1 2 The fall distance is 10 m d = gt = 2 ( 0.15 s) = s.1125 m Answer A. 15. In a speedometer test zone on a highway, you drive 5 miles in 6 minutes. During the test, your speedometer reading is 55 mi/hr. Your speedometer reading is A) lower than your actual speed. B) equal to your actual speed. C) higher than your actual speed. 5 The average speed is S = d = mi = 50 mi since 6 minutes is 0.1 hour. The answer is C. t 0.1Hr hr 16. All except one of the following require the application of a net force. Which one is the exception? A) to change an object from a state of rest to a state of motion. B) to maintain an object in motion at a constant velocity. C) to change an object's speed without changing its direction of motion. D) to maintain an object in uniform circular motion. E) to change an object's direction of motion without changing its speed. This is an application of Newtons 1 st law. No force is required to maintain an object in motion at constant velocity. The answer is B. 17. Assuming g = 10 m/s² and that air resistance is negligible, in ½ second a ball dropped from rest will fall A) ½ meter. B) one meter. C) 1.25 meters. D) 5 meters. 1 2 1 2 10 m d = gt = 2 ( 0.5 s) = s 1.25 m Answer C. Page 4
18. A refrigerator weighing 1500 N is to be lifted onto a truck bed that is 1.0 m above the ground. When pushed up a slanting ramp 2.0 m in length a force of only 800 N is required to move it at constant velocity. Comparing the work involved in lifting the refrigerator straight up to the work in pushing it along the ramp, there is A) less work required when the ramp is employed. B) more work required when the ramp is employed. C) an equal amount of work is required in each case. W=F*d. The work of lifting directly is 1500N*1m=1500J. The work of sliding on the ramp is 2m*800N= 1600J. The answer is B. 19. In Vienna, there is a Ferris wheel designed so that the passengers ride in a standing position. If one of the passengers were standing on a bathroom scale, the scale would read lowest at A) the highest point in the ride. B) the lowest point in the ride. C) the point in the ride where they were ascending most rapidly. D) the point in the ride where they were descending most rapidly. The centripetal acceleration is toward the center of the circular wheel. In such motion you feel a centrifugal force that is in the opposite direction. Gravity pulls down and when you are at the top of the circle the centrifugal force is pulling you directly up relative to the scale. So the answer is A. 20. A ball rolls off a shelf and hits the floor below 0.25 seconds later. To find the speed of the ball as it left the shelf, we would need A) the distance measured along the floor to the point of impact. B) to repeat the experiment. C) the height of the shelf. D) the weight of the ball. From the fall time you can tell how high up the shelf is. If you knew the distance d measured along the floor to the point of impact you could determine the (constant) horizontal speed from d vx = The answer is A. falltime Page 5
Answer Key 1. C 2. D 3. E 4. C 5. D 6. C 7. C 8. B 9. C 10. B 11. D 12. C 13. B 14. A 15. C 16. B 17. C 18. B 19. A 20. A Page 6