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Conceptual questions

Explain the meaning of the terms “red shift” and “blue shift” as they relate to the relativistic Doppler effect.

What happens to the relativistic Doppler effect when relative velocity is zero? Is this the expected result?

Is the relativistic Doppler effect consistent with the classical Doppler effect in the respect that λ obs size 12{λ rSub { size 8{"obs"} } } {} is larger for motion away?

All galaxies farther away than about 50 × 10 6 ly size 12{"50" times "10" rSup { size 8{6} } `"ly"} {} exhibit a red shift in their emitted light that is proportional to distance, with those farther and farther away having progressively greater red shifts. What does this imply, assuming that the only source of red shift is relative motion? (Hint: At these large distances, it is space itself that is expanding, but the effect on light is the same.)

Problems&Exercises

Suppose a spaceship heading straight towards the Earth at 0 . 750 c size 12{0 "." "750"c} {} can shoot a canister at 0 . 500 c size 12{0 "." "750"c} {} relative to the ship. (a) What is the velocity of the canister relative to the Earth, if it is shot directly at the Earth? (b) If it is shot directly away from the Earth?

(a) 0 . 909 c size 12{0 "." "909"c} {}

(b) 0 . 400 c size 12{0 "." "400"c} {}

Repeat the previous problem with the ship heading directly away from the Earth.

If a spaceship is approaching the Earth at 0.100 c and a message capsule is sent toward it at 0.100 c relative to the Earth, what is the speed of the capsule relative to the ship?

0 . 198 c size 12{0 "." "198"c} {}

(a) Suppose the speed of light were only 3000 m/s . A jet fighter moving toward a target on the ground at 800 m/s shoots bullets, each having a muzzle velocity of 1000 m/s . What are the bullets’ velocity relative to the target? (b) If the speed of light was this small, would you observe relativistic effects in everyday life? Discuss.

If a galaxy moving away from the Earth has a speed of 1000 km/s size 12{1,"000"" m/s"} {} and emits 656 nm size 12{"656"" nm"} {} light characteristic of hydrogen (the most common element in the universe). (a) What wavelength would we observe on the Earth? (b) What type of electromagnetic radiation is this? (c) Why is the speed of the Earth in its orbit negligible here?

a) 658 nm size 12{"658""nm"} {}

b) red

c) v / c = 9 . 92 × 10 5 size 12{v/ ital "c="9 "." "92" times "10" rSup { size 8{ - 5} } } {} (negligible)

A space probe speeding towards the nearest star moves at 0 . 250 c size 12{0 "." "250"c} {} and sends radio information at a broadcast frequency of 1.00 GHz. What frequency is received on the Earth?

If two spaceships are heading directly towards each other at 0 . 800 c size 12{0 "." "800"c} {} , at what speed must a canister be shot from the first ship to approach the other at 0 . 999 c size 12{0 "." "999"c} {} as seen by the second ship?

0 . 991 c size 12{0 "." "991"c} {}

Two planets are on a collision course, heading directly towards each other at 0 . 250 c size 12{0 "." "250"c} {} . A spaceship sent from one planet approaches the second at 0 . 750 c size 12{0 "." "750"c} {} as seen by the second planet. What is the velocity of the ship relative to the first planet?

When a missile is shot from one spaceship towards another, it leaves the first at 0 . 950 c size 12{0 "." "950"c} {} and approaches the other at 0 . 750 c size 12{0 "." "750"c} {} . What is the relative velocity of the two ships?

0 . 696 c size 12{0 "." "696"c} {}

What is the relative velocity of two spaceships if one fires a missile at the other at 0.750 c and the other observes it to approach at 0.950 c ?

Near the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive 1900 nm electromagnetic radiation and know that it was 1875 nm when emitted by the hydrogen gas. What is the speed of the gas?

0 . 01324 c size 12{0 "." "01324" c} {}

A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.

Prove that for any relative velocity v size 12{v} {} between two observers, a beam of light sent from one to the other will approach at speed c size 12{c} {} (provided that v size 12{v} {} is less than c size 12{c} {} , of course).

u = c , so

u = v+u 1 + ( vu ′/ c 2 ) = v+c 1 + ( vc / c 2 ) = v+c 1 + ( v / c ) = c ( v+c ) c+v = c size 12{alignl { stack { ital "u=" { { ital "v+u'"} over {1+ \( ital "vu""'/"c rSup { size 8{2} } \) } } = { { ital "v+c"} over {1+ \( ital "vc"/c rSup { size 8{2} } \) } } = { { ital "v+c"} over {1+\( v/c \) } } {} # { {c \( ital "v+c" \) } over { ital "c+v"} } = {underline {c}} {}} } } {}

Show that for any relative velocity v size 12{v} {} between two observers, a beam of light projected by one directly away from the other will move away at the speed of light (provided that v size 12{v} {} is less than c size 12{c} {} , of course).

(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12 . 0 × 10 9 ly size 12{"12" "." 0 times "10" rSup { size 8{9} } " ly"} {} ly away is receding from us at 0. 0.900 c , at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990 c , as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from the Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)

a) 0 . 99947 c

b) 1 . 2064 × 10 11 y size 12{1 "." "2064" times "10" rSup { size 8{"11"} } " y"} {}

c) 1 . 2058 × 10 11 y size 12{1 "." "2058" times "10" rSup { size 8{"11"} } " y"} {} (all to sufficient digits to show effects)

Questions & Answers

Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
How we can toraidal magnetic field
Aditya Reply
How we can create polaidal magnetic field
Aditya
4
Mykayuh Reply
Because I'm writing a report and I would like to be really precise for the references
Gre Reply
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!
Gre Reply
Practice Key Terms 3

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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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