Please help with Length Dilation (1 Viewer)

[sean182]

Hey, can someone please explain to me about Length Dilation?

what does the Tv and To represent?

theres these 2 questions that are confusing

one asks wat is the distance travelled by a muon at an extremely high speed, and the answer is 44m which has been reduced from 100km due to length dilation

the other question says that an astronaut on a speeding ship will measure his craft to be 10.9 m whilst observeser will see the space ship as about 10m. But if the astronaut is moving at a high speed, doesnt length contract for him?

i dont get it because in one question, the object with the high speed has travelled a much shorter distance due to length dilation, but in another question, a man on an obejct travelling at high speed measures his craft to be longer than what an observer would see it as.

so how do u know what the value for Tv and To is?

thanks to anyone who can help me

 

[simbim21]

it all comes down to the frame of reference- you have to read the question carefully

Lenght conraction means that at relativistic speeds, the length of an object will appear to contract to an observer OUTSIDE the object's frame of reference (and moving relative to the object)

'Lo' refers to the original (o) length of the object as seen by the observer in the object's frame of reference. Hence, the astronaut sees his craft as 10.9m (original lenght since it is seen by an observer on the craft), whilst an observer in an external frame of reference sees it contract to its relativistic length (Lv), which is 10m.

Same situation with the muon. To the muon, it thinks it needs to travel 100km (Lo). to an external observer, however, this length appears shorter- 44km (Lv).

and Lv can be figured out by that big looking equation that i'm sure you've seen

I know it's confusing, but i hope that helps

 

[ianc]

okay for starters you HAVE to get your terminology right otherwise you will lose marks in exams:
- Time Dilation
- Length Contraction
- Mass Dilation

(Dilation means getting bigger, contracting means getting smaller)

As simbim21 said, the L_o is the length of the object as seen when the object is stationary and L_v is the length of the moving object as observed by the same "stationary" observer.

The same rules apply for t_o and t_v and m_o and m_v.

Hope this helps!

 

[Forbidden.]

Oh man I definitely will be beating a lot of people in the Physics HSC ....

Anyway I what I think of _v & ₀...

The _v subscript refers to a moving object, relative to you. (e.g m_v, t_v & l_v).

The ₀ subscript refers to the object when it is at rest, relative to you.
This also applies to the moving object relative to it, regardless whether it is moving or not (e.g m₀, t₀ & l₀).

 

[airie]

But all those "at rest" and "moving" assertions are relative. It'll be safer to say that the _o subscripts is for the quantities as measured in the same reference frame as the event, and the _v subscript is for the quantities measured in another frame of reference in constant motion with respect to the event's frame.

 

[watatank]

Oh man I definitely will be beating a lot of people in the Physics HSC ....

Whether its true or not there's no need for that...if you're going to post just answer the question.

 

[nounderscore]

Oh man I definitely will be beating a lot of people in the Physics HSC ....

LOLS