Speed for a meter stick to contract to 0.5 meters

[Tonia]

Homework Statement

How fast must a meter stick be moving of its length is measured to shrink to 0.500 meters?

Homework Equations

v/c = sqrt(1 - (1/L)^2) = sqrt(1 - 1/4) = sqrt(3/4) = sqrt(3)/2 or use v = sqrt(3)c/2

The Attempt at a Solution

(squrt 3c/2) = squrt 450000000 = 21213.203 = 21213.2 km/sec.

 

[Orodruin]

You have taken sqrt(3c/2) instead of sqrt(3) c/2 ... The square root of a velocity can never be a velocity.

 

[Tonia]

So it's (sqrt of 3)/(c/2)??

 

[Orodruin]

No, your original math when arriving at sqrt(3) c/2 was correct. What you did not do correctly was inserting numbers into this formula. There is a difference between sqrt(3) c/2 and sqrt(3c/2)...

 

[Tonia]

So my answer is correct? I still don't understand.

 

[Orodruin]

No, it is not correct. What part of sqrt(3) c/2 is not equal to sqrt(3c/2) do you find confusing.

 

[Tonia]

After I take the square root of 3, I multiply that by the c/2??

 

[Orodruin]

Yes, this is what your expression tells you to do.

 

[Tonia]

1.7320 times c/2 = 1.7320 times 150,000,000 = 2.598E8 = 2.598 X 10^8 km/sec

 

[Orodruin]

Better, but as you are giving the speed of light with one significant digit, you really should not have four significant digits in your answer.

 

[Tonia]

1.7 times 150,000,000 = 2.55E^8 = 2.5 X 10^8 km/sec.

 

[Orodruin]

You should always keep all digits in intermediate steps, otherwise your results will contain rounding errors which can propagate and amplify. The more correct thing to do would be to simply round the final result down to two significant digits.

 

[Tonia]

Other than that my answer is correct?