Week 11 weekly assignment
Week 11 weekly assignment 1220
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This 8 page Class Notes was uploaded by Dragon Note on Wednesday April 6, 2016. The Class Notes belongs to 1220 at University of Missouri - Columbia taught by Y Zhang in Spring 2016. Since its upload, it has received 522 views. For similar materials see College Physics II in Physics 2 at University of Missouri - Columbia.
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Date Created: 04/06/16
Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... Weekly Assignment 11 (included in Exam 3) Due: 9:00pm on Monday, April 11, 2016 To understand how points are awarded, read the Grading Policy for this assignment. CE Predict/Explain 29.1 You are in a spaceship, traveling directly away from the Moon with a speed of 0.9 . A light signal is sent in your direction from the surface of the Moon. Part A As the signal passes your ship, do you measure its speed to be greater than, less than, or equal to 0.1 ? ANSWER: greater than less than equal to Correct Part B Choose the best explanation from among the following: ANSWER: The speed you measure will be greater than 0.1 ; in fact, it will be , since all observers in inertial frames measure the same speed of light. You will measure a speed less than 0.1 because of time dilation, whch causes clocks to run slow. When you measure the speed you will find it to be 0.1 , which is the difference and 0.9 . Correct Problem 29.2 Albert is piloting his spaceship, heading east with a speed of 0.87 . Albert's ship sends a light beam in the forward (eastward) direction, which travels away from his ship at a speed . Meanwhile, Isaac is piloting his ship in the westward direction, also at 0.87 , toward Albert's ship. Part A With what speed does Isaac see Albert's light beam pass his ship? ANSWER: 1.00 All attempts used; correct answer displayed Problem 29.9 As a spaceship flies past with speed , you observe that 1.0elapses on the ship's clock in the same time that 1.000elapses on Earth. Part A How fast is the ship traveling, relative to the Earth? (Express your answer as a fraction of the speed of light.) Express your answer using five significant figures. ANSWER: Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... = 0.99986 Correct Conceptual Exercise 29.3 A street performer tosses a ball straight up into the air (event 1) and then catches it in his mouth (event 2). Part A For each of the following observers, state whether the time they measure between these two events is the proper time or the dilated time. ANSWER: Correct Problem 29.8 Astronaut Benny travels to Vega, the fifth brightest star in the night sky, leaving his 35.0-year-old twin sister Jenny behind on Earth. Benny travels with a speed of 0.9994 , and Vega is 25.3 light-years from Earth. Part A How much does Benny age when he arrives at Vega? ANSWER: 10.5 Correct Lifetime of the Speeding Muon One of the many fundamental particles in nature is the. This particle acts very much like a "heavy electron." It has a mass of , Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... compared to the electron's mass of just . (We are using to obtain the mass in units of energy and the speed of light ). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos ( ). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about( ). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Let's begin by considering some muons moving at various speeds relative to a stationary observer. Part A If a muon is traveling at 70% of the speed of light, how long does it take to decay in the observer's rest frame (i.e., what is the observed liof the muon)? Express your answer in microseconds to two significant figures. Hint 1. Effects of velocity on time Recall that clocks in motion relative to an observer will always appear to run slower than the clock in the observer's rest frame by a factor of . Hint 2. Definition of factor The effect of time dilation is to slow down a moving clock by a factor of , where . Notice that for all velocities. ANSWER: = 3.1 Correct Part B If a muon is traveling at 99.9% the speed of light, how long will it take to decay in the observer's rest frame (i.e., what is the observed of theme muon)? Express your answer in microseconds to two significant figures. ANSWER: = 49.2 All attempts used; correct answer displayed A stream of particles, often called cosmic rays, is constantly raining down on the earth from outer space. Most cosmic-ray particles are protons. When they crash into the upper atmosphere, they can convert into particles called pions ( ), which subsequently decay into muons. These muons can then continue toward the earth until they, too, decay. Let us consider the effects of time dilation on the cosmic rays. Suppose that a cosmic-ray proton crashes into a nitrogen molecule in the upper atmosphere, 45 km above the earth's surface, producing a pion that decays into a muon. Assume that the muon has a downward velocity of 99.9943% the speed of light. Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part C How far ( ) would the muon travel before it decayed, if there were no time dilation? Express your answer in meters to three significant figures. ANSWER: = 659 All attempts used; correct answer displayed Part D Now, let us consider the effects of time dilation. How far would the muon travel, taking time dilation into account? Express your answer in kilometers to two significant figures. ANSWER: = 62 All attempts used; correct answer displayed Notice how huge the effect of time dilation is on the propagation of these cosmic-ray secondary particles. The large time dilation allows the muons to reach the surface of the earth in enormous quantities. They actually comprise a fairly substantial background for some types of particle experiments, requiring the experiments to be placed underground. The pions, however, decay 100 times faster than the muons, and consequently they almost never make it to the earth's surface, even with a large time dilation. Pendulums in Relative Motion Two identical pendulums have the same period when measured in the factory. While one pendulum swings on earth, the other is taken on a spaceship traveling at 95 the speed of light. Assume that both pendulums operate under the influence of the same net force and swing through the same angle. Part A When observed from earth, how many oscillations does the pendulum on the spaceship undergo compared to the pendulum on earth in a given time interval? Hint 1. How to approach the problem When observed in their rest frame of reference, the pendulums undergo the same number of oscillations in a given time interval. For example, when the pendulums are both in the factory, the time interval between oscillations (the period) is the same for both pendulums. However, the pendulum on the spaceship is moving with respect to the earth, so when observed from earth, the time interval between oscillations will no longer be the same for the two pendulums. Will it be longer or shorter? Hint 2. Relativistic time dilation If two events occur at the same point in space in a particular frame of reference, an observer in a second frame moving with constant velocity relative to the first frame measures a longer time interval between the events. This effect is called time dilation. Hint 3. Period of oscillation Recall that the period of a pendulum is defined as the time it takes the pendulum to undergo one complete oscillation. ANSWER: more oscillations fewer oscillations the same number of oscillations Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Because of the effect of time dilation, an observer on earth will measure a longer time interval between the oscillations completed by the pendulum on the spaceship than by the pendulum on earth. This means that, in a given time interval, the observer on earth will see the pendulum on the spaceship oscillate fewer times than the pendulum on earth. Part B If each pendulum is part of a clock, such that every oscillation of the pendulum corresponds to a tick of the clock, when observed from earth, which clock runs faster? Hint 1. How to approach the problem As you found out in the previous part, when observed from earth, the pendulum on the spaceship takes longer to complete one oscillation. Since each oscillation is a tick of the clock, then, simply identify the clock that runs faster.. ANSWER: the clock on earth the clock on the spaceship neither; the two clocks show the same time Correct Because of the effect of time dilation, a clock moving with respect to an observer appears to run more slowly than a clock that is at rest in the observer's frame. Note that the situation can be reversed if a different frame of reference is used. For example, since the clock on earth is moving relative to the spaceship, an astronaut on the ship would observe the clock on the spaceship to be running faster than the clock on earth. Problem 29.16 An observer moving toward Earth with a speed of 0.96 notices that it takes 5.2for a person to fill her car with gas. Suppose, instead, that the observer had been moving away from Earth with a speed of 0.80 . Part A How much time would the observer have measured for the car to be filled in this case? Express your answer using two significant figures. ANSWER: = 2.4 All attempts used; correct answer displayed Problem 29.20 5 As measured in Earth's frame of reference, two planets are 4.24×10 apart. A spaceship flies from one planet to the other with a constant velocity, and the clocks on the ship show that the trip lasts only.1.01 Part A How fast is the ship traveling? ANSWER: = 2.44×108 Correct Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... How Tall Really Is Your Favorite Superhero? You are at the top of the Empire State Building on the 102nd floor, which is located 37above the ground, when your favorite superhero flies over the building parallel to the ground at 60.0the speed of light. Part A You have never seen your favorite superhero in real life. Out of curiosity you calculate her height to be 1. If the superhero landed next to you, how tall would she be when standing? Hint 1. How to approach the problem When you estimate how tall the superhero is while she is flying over the building, you are calculating a distance between two points (the distance between the bottom of her feet and the top of her head) that are both in motion relative to you. Moreover, you are calculating a distance in a direction parallel to the relative motion. Your estimate will therefore be affected by the relativistic effect of length contraction. In contrast, when measuring the height of the superhero standing next to you, you calculate the distance between the same two points that are at rest relative to you, which is the proper length. Hint 2. Length contraction parallel to motion The distance between two points at rest in a particular frame of reference S iwhen measured by an observer at rest in that frame. An observer moving at speed relative to S, instead, measures the same distance to be , where is the speed of light. Hint 3. Find the speed of the superhero What is the speed of the superhero when she flies at 60.0 the speed of light? Express your answer in units of , the speed of light. For example, if the superhero travels with a speed of , enter only 0.30. ANSWER: = 0.600 ANSWER: 2.00 1.60 1.26 1.28 Correct When standing next to you, the superhero is at rest relative to you, so her height is a proper length. When she is flying, you will measure her height to be shorter because of length contraction. Part B What is the height of the 102nd floor of the Empire State Building as measured by the superhero while flying above it? Hint 1. How to approach the problem Because the superhero is flying parallel to the ground, the building is moving relative to the superhero at a speed 0in a direction perpendicular to its height. To calculate the height of the building, the superhero has to measure the distance between the top floor and the ground. This distance is measured in a direction perpendicular to the relative motion. Does length contraction take place in the superhero's observation? ANSWER: Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... 373 298 236 239 Correct Since the superhero is flying parallel to the ground, when she estimates the height of the building, she is measuring a distance in a direction perpendicular to the relative motion. Therefore, she will not observe any length contraction. Problem 29.24 Part A How fast does a 260 spaceship move relative to an observer who measures the ship's length to b? 140 Express your answer using two significant figures. ANSWER: = 0.84 All attempts used; correct answer displayed Problem 29.26 A rectangular painting is 125wide and 72.1 high, as indicated in the figure. Part A At what speed, , must the painting move parallel to its width if it is to appear to be square? ANSWER: = 0.817 Correct Problem 29.28 A cubical box is 0.66on a side. Part A What are the dimensions of the box as measured by an observer moving with a speed oparallel to one of the edges of the box? Express your answers using two significant figures separated by commas. Weekly Assignment 11 (included in Exam 3) https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: , , = 0.27,0.66,0.66 All attempts used; correct answer displayed Part B What is the volume of the box, as measured by this observer? Express your answer using two significant figures. ANSWER: = 0.12 Correct Problem 29.30 An astronaut travels to a distant star with a speed orelative to Earth. From the astronaut's point of view, the stfrom Earth. On the return trip, the astronaut travels with a speed ofrelative to Earth. Part A What is the distance covered on the return trip, as measured by the astronaut? Give your answer in light-years. Express your answer using two significant figures. ANSWER: = 3.2 Correct Problem 29.33 A ladder 4.9 long leans against a wall inside a spaceship. From the point of view of a person on the ship, the base of thefrom the wall, and the top of the ladder is 3above the floor. The spaceship moves past the Earth with a speed ofin a direction parallel to the floor of the ship. Part A Find the angle the ladder makes with the floor as seen by an observer on Earth. Express your answer using two significant figures. ANSWER: = 70 Correct Score Summary: Your score on this assignment is 71.7%. You received 10.75 out of a possible total of 15 points.
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