Chap R SM - Chapter R Relativity Conceptual Problems 1 You...

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Chapter R Relativity Conceptual Problems 1 You are standing on a corner and a friend is driving past in an automobile. Each of you is wearing a wristwatch. Both of you note the times when the car passes two different intersections and determine from your watch readings the time that elapses between the two events. Have either of you determined the proper time interval? Explain your answer. Determine the Concept In the reference frame of the car both events occur at the same location (the location of the car). Thus, your friend’s watch measures the proper time between the two events. 2 In Problem 1, suppose your friend in the car measures the width of the car door to be 90 cm. You also measure the width as he goes by you. ( a ) Does either of you measures the proper width of the door? Explain your answer. ( b ) How will your value for the door width compare to his? (1) Yours will be smaller, (2) yours will be larger, (3) yours will be the same, (4) you can’t compare the widths, as the answer depends on the car’s speed. Determine the Concept The proper length of an object is the length of the object in the rest frame of the object. The proper length of a meter stick is one meter. ( a ) Because the door is at rest in the reference frame of the car, its width in that frame is its proper width. If your friend measures this width, say by placing a meter stick against the door, then he will measure the proper width of the door. ( b ) In the reference frame in which you are at rest, the door is moving, so its width is less than its proper width. To measure this width would be challenging. (You could measure the width by measuring the time for the door to go by. The width of the door is the product of the speed of the car and the time.) 3 [SSM] If event A occurs at a different location than event B in some reference frame, might it be possible for there to be a second reference frame in which they occur at the same location? If so, give an example. If not, explain why not. Determine the Concept Yes. Let the initial frame of reference be frame 1. In frame 1 let L be the distance between the events, let T be the time between the events, and let the + x direction be the direction of event B relative to event A. Next, calculate the value of L/T . If L/T is less than c , then consider the two events in a reference frame 2, a frame moving at speed v = L/T in the + x direction. In frame 2 both events occur at the same location. 1051
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Chapter R 1052 4 [SSM] If event A occurs prior to event B in some frame, might it be possible for there to be a second reference frame in which event B occurs prior to event A? If so, give an example. If not, explain why not. Determine the Concept Yes. Let L and T be the distance and time between the two events in reference frame 1. If L cT , then something moving at a speed less than or equal to c could travel from the location of event A to the location of event B in a time less than T . Thus, it is possible that event A could cause event B. For events like these, causality demands that event A must precede event B in
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Chap R SM - Chapter R Relativity Conceptual Problems 1 You...

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