Section 9 - Length contraction
9.1 A newly-constructed spaceliner boasts a 105 m long and 65.0 m wide soccer field for the enjoyment of its international crew
during extended missions. The long dimension of the soccer field is aligned along the ship's direction of flight. As the ship
cruises by Earth, FIFA (Fédération Internationale de Football Association) officials on Earth measure the length of the field as
99.0 m and declare the field ineligible since it is shorter than the required 100 m. The captain protests that the discrepancy is
due to length contraction. (a) How fast was the ship traveling according to the Earth-bound observers (as a decimal fraction of
c)? (b) What is the width of the field according to the FIFA officials?
(a) c
(b) m
9.2 You want to visit your friend Ford Prefect, who lives in the vicinity of Betelgeuse, 425 light-years from Earth (that is, light
takes 425 years to arrive from Betelgeuse). You hitch a ride on a passing starcruiser, and as measured by Earth observers,
you travel so fast that the trip only takes 426 years. (a) How long was the trip according to you? (b) What is the distance
between Betelgeuse and Earth, according to you?
(a) years
(b) light-years
Section 10 - Doppler shift for light
10.1 A spaceship is flying directly away from Earth at a speed of 0.725c, and the captain's family at home on Earth broadcasts
their well wishes on the Family Radio System frequency of 462.5625 Mhz. To what frequency must the homesick captain tune
the ship's radio to receive the broadcast? (Round your answer to three significant figures.)
MHz
10.2 Starting in Toronto, Canada, a spaceship flies down Yonge Street (reportedly the longest street in the world) at a velocity of
0.330c. An astronaut on board measures her pulse rate at 50.0 beats per minute. (a) What is the time interval between
heartbeats according to her? (b) What is the time interval between beats according to observers who are standing by the side
of the road? Now, the astronaut is attached to a machine that sends a brief radio pulse for each beat of her heart back toward
a monitoring device at her starting point. (c) What is the time interval measured by the monitor between consecutive radio
pulses?
(a) s
(b) s
(c) s10.3 Albert protests the $150 ticket he received for piloting his spaceship through a red light (wavelength Ȝ = 630 nm) on
Intergalactic-5. His argument is that he was moving so quickly toward the light that it appeared to have a wavelength ofȜ = 546 nm, which is green. The judge agrees to dismiss the ticket, but instead fines him for speeding. The speed limit is
5.0% of c, with a charge of $20 for each percentage point in excess of that (for example, a speed of 0.085c = $70 ticket). (a)
How fast was Albert traveling down the highway? Express your answer as a decimal fraction of c. (b) How much does he
have to pay?
(a) c
(b) $10.4 A police sergeant has set up a speed trap on the popular Rocketbahn route. While she is idling next to a signpost, she fires
her 12.0 GHz radar gun at an oncoming sports rocket that is heading directly toward her. The radar wave hits the rocket,
reflects off it, and returns directly to her detector. She detects a reflected frequency of 15.0 GHz. At what speed is the sports
rocket traveling? Express your answer as a decimal fraction of c.
c
Section 12 - Mass and energy
12.1 Find the (a) speed (as a decimal fraction of c) and (b) momentum of a proton that has a kinetic energy of 1000 MeV. The
proton mass is 1.673×10í^27 kg, or 938 MeV/c^2.
(a) c
(b) MeV/c12.2 On the television show Star Trek®, a handheld device called a phaser vaporizes humanoid-sized bad guys, presumably
turning their mass into energy, with no ill effects to the operator or to nearby objects. On the show, the energy is represented
by a brief, glowing outline. In the real world, if a 50 kg alien were turned completely into energy, the energy released would be
equal to how many tons of exploding TNT? The explosion of one ton of TNT releases approximately 4.0×10^9 joules of energy.
tons of TNT