Earth. Astronaut Naomi sends a laser pulse from the tail of the rocket to the nose, where it reflects off a mirror, and returns to
Naomi. (a) How long does the round trip take, according to Naomi? (b) How long does the round trip take according to Tariq,
an observer on Earth?
(a) s
(b) s
6.2 An interstellar spacecraft races by the Earth at a velocity of 1.85×10^8 m/s, as measured by observers on the Earth. The
spacecraft's galley cook places a pot of Minute® rice on the stove for exactly 60.0 s, according to his watch. How long will the
pot have been on the stove according to the earthbound observers?
s
6.3 An interstellar cruise ship races by a Martian spaceport. According to galactic regulations, the safety strobe lights on the
ship's bridge are supposed to blink every 1.50 seconds. A rookie policemartian, based on the planet, issues a ticket, claiming
he measured the time interval between blinks as 1.75 seconds. You are called upon by the indignant captain to explain the
discrepancy, who maintains that her lights are fully compliant with code. What spacecraft speed will show both the captain
and policemartian to be correct?
m/s
6.4 You have probably never noticed time dilation effects in everyday life. Do some calculations to see why this is. (a) Calculate
the speed that a friend would have to move with respect to you so that your measured time intervals are 1.00% larger than
hers. That is, for each 100 elapsed seconds on her wristwatch, 101 seconds elapse on yours. (b) How many times larger is
the speed you just calculated than the speed of an orbiting space shuttle, 8.00×10^3 m/s?
(a) m/s
(b) times the speed of the shuttle
6.5 A pi meson, or pion, is an elementary particle that exists for a brief time. Charged pions at rest have an average lifetime of
26.0 ns. A group of freshly created pions travel, each at a constant speed, an average distance of 28.0 m in the laboratory
before decaying. What was the average pion speed as measured in the lab?m/sSection 7 - Exploring and deriving time dilation
7.1 Consider a very tall light clock that is 555 meters high. It is mounted vertically on a spacecraft that is moving along the
positive x axis at 2.00×10^8 m/s, as measured from the Earth. During a certain time interval, an earthbound observer measures
the clock moving a distance of 497 meters along the x axis, while the light pulse has made a trip from the bottom of the clock
to the top. (a) How far has the light pulse traveled, according to an astronaut on the spacecraft? (b) How far has the light
pulse traveled, according to earthbound observers? (Your answers to parts a and b should differ.) (c) What is the time interval
required for the light pulse to travel from the bottom to the top of the clock, according to the astronaut? (d) What is the time
interval required for the light pulse to travel from the bottom to the top of the clock, according to earthbound observers? (e)
Calculate the Lorentz factor for the spacecraft. (f) Use the Lorentz factor to calculate the dilated time interval corresponding to
the astronaut's measurement in part c. (Your answers to parts d and f should be the same.)
(a) m
(b) m
(c) s
(d) s
(e)
(f) sSection 8 - Interactive problem: Experiment with the light clock
8.1 Use the simulation in the interactive problem in this section to answer the following questions. (a) How long does the
professor think it took him to cross the basketball court? (b) How long does Kathering think it took the professor to cross the
basketball court? (c) Suppose Katherine measures the length of the court as 24.0 m, and then uses this to calculate the
professor's speed. If the professor uses that value for his speed and the time hemeasured, is the professor's measurement of
the basketball court's length going to be longer, shorter or the same as Katherine's measurement?
(a) s
(b) s
(c) i. Longer
ii. Shorter
iii. The same length(^656) Copyright 2000-2007 Kinetic Books Co. Chapter 35 Problems