Question

A rod 1m long moves with a velocity of 0.6c.Calculate it's length as it appears to an observer on the earth?

Answer 1

`0.8m`

Explanation:

An object moving at a speed `v` relative to an observer will appear to contract from both frames of reference, though with the object's frame of reference it is the observer being contracted. This happens all the time but the speeds are always too slow to have any noticeable effect, only being noticeable at relativistic speeds.

Formula for length contraction is `L=L_0sqrt(1-v^2/c^2)`, where:

• `L` = new length (`m`)
• `L_0` = original length (`m`)
• `v` = speed of object (`ms^-1`)
• `c` = speed of light (`~3.00*10^8ms^-1`)

So,
`L=sqrt(1-(0.6c)^2/c^2)`

`=sqrt(1-0.6^2)`

`=sqrt(1-0.36)`

`=sqrt0.64`

`=0.8m`