# How fast must a meter stick be moving if its length is....

1. Jun 7, 2015

### Tonia

1. The problem statement, all variables and given/known data
How fast must a meter stick be moving of its length is measured to shrink to 0.500 meters?

2. Relevant 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

3. The attempt at a solution
(squrt 3c/2) = squrt 450000000 = 21213.203 = 21213.2 km/sec.

2. Jun 7, 2015

### Orodruin

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

3. Jun 7, 2015

### Tonia

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

4. Jun 7, 2015

### Orodruin

Staff Emeritus
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)...

5. Jun 7, 2015

### Tonia

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

6. Jun 8, 2015

### Orodruin

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

7. Jun 8, 2015

### Tonia

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

8. Jun 8, 2015

### Orodruin

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

9. Jun 8, 2015

### Tonia

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

10. Jun 8, 2015

### Orodruin

Staff Emeritus
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.

11. Jun 8, 2015

### Tonia

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

12. Jun 8, 2015

### Orodruin

Staff Emeritus
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.

13. Jun 8, 2015

### Tonia

Other than that my answer is correct?