Acceleration of gravity measured

[Robb]

Homework Statement

A simple pendulum is used to measure the acceleration of gravity using T= 2pi sqrt(l/g). The period was measured to be 1.24 +-0.02s and the length, l, to be 0.381 +-0.002m. What is the resulting value for g with it's absolute and relative uncertainty?

Homework Equations

T= 2pi sqrt(l/g)

The Attempt at a Solution

1.24= 2pi sqrt(.381/g)--------g=.381m/3.794m/s^2

 

[haruspex]

Homework Statement

A simple pendulum is used to measure the acceleration of gravity using T= 2pi sqrt(l/g). The period was measured to be 1.24 +-0.02s and the length, l, to be 0.381 +-0.002m. What is the resulting value for g with it's absolute and relative uncertainty?

Homework Equations

T= 2pi sqrt(l/g)

The Attempt at a Solution

1.24= 2pi sqrt(.381/g)--------g=.381m/3.794m/s^2

You seem to have made an error in that calculation. Please post all your steps.
With regard to the error calculation, you need to show an attempt at that too.
There are two different ways of determining resultant error, and which is correct depends on what the answer will be used for. An engineer mostly takes 'worst case', i.e. the extreme possibilities of the result given the ranges of the input errors. In other environments, a more statistical approach is used, and the formula involves root-sum-square. Which have you been taught?

 

[Robb]

T= 2pi sqrt(l/g)
1.24= 2pi sqrt(.381/g)
(1.24/2pi)=sqrt(.381/g)
(1.24/2pi)^2=.381/g
g=.381/3.794
g=.100m/s^2

I assume the uncertainty to be 0.002+0.02=0.022. I believe the relative uncertainty would be determined after I have found the value for g.

 

[SteamKing]

T= 2pi sqrt(l/g)
1.24= 2pi sqrt(.381/g)
(1.24/2pi)=sqrt(.381/g)
(1.24/2pi)^2=.381/g
g=.381/3.794
g=.100m/s^2

I assume the uncertainty to be 0.002+0.02=0.022. I believe the relative uncertainty would be determined after I have found the value for g.

You've made a mistake in your arithmetic.

You have calculated [(1.24 / 2)*π]² = 0.381 / g, rather than [1.24 / (2π)]² = 0.381 / g

 

[Robb]

I guess I'm not sure the difference? They both are both equal: g=.381/3.794. Correct?

 

[SteamKing]

I guess I'm not sure the difference? They both are both equal: g=.381/3.794. Correct?

No, they don't.

(1.24 / 2) * π = 0.62 * π =1.95

1.24 / (2π) = 1.24 / (6.28) = 0.197

When you square each result, you get quite different numbers

You've got to learn how to use parentheses correctly in your arithmetic.

 

[Robb]

Wow! I guess I needed another set of parenthesis for the 2pi! Thanks so much for the help.

 

[SteamKing]

Wow! I guess I needed another set of parenthesis for the 2pi! Thanks so much for the help.

It makes quite a difference in the value of g calculated from this experiment.