Length Contraction


We have discussed the effects of relativistic speeds on time now let's have a look on its effect on length. To get straight to the point the length of an object will contract (in the direction parallel to its motion) when traveling at relativistic speeds. This "shortening" of length is called length contraction. The equation for calculating the length as seen by an outside observer is as follows:


L = L0((1 - v2/c2))1/2


where: L = the length measured by the "other" observer

L0 = the length measured by the observers on reference frame

v = the speed of the object

c = the speed of light in a vacuum


Look at the following example:

A observer on earth sees a rocket zoom by at .95c. If the rocket is measured to be 5.5 m in length, how long is the rocket ship as measure by the astronaut inside the rocket?

L = 5.5 m

v = .95c

L0 = ?

solving: 5.5 = L0×(1- .95c2/c2)

5.5 = L0×(.312)

L0 = 5.5/(.312) = 17.6 m

Hint: When working these problems be sure to think about what the answer should look like. That is in this case I knew that the length measured by the astronaut had to be larger than that measured by the earth bound person. So if I got L and Lo confused I would have realized it when I got a smaller number. Just understand the concept and then think about your answer!

Now once again notice that at small speeds the quantity v2/c2 approaches 0 and L = L0, but at high speeds the quantity approaches one (but never reaches it) therefore causing L to become smaller and smaller! Once again think about it!


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