Physics Experiment: Calculating G from T

[donniemateno]

morning ladies n gents

just wondering has anyone studied this physics experiment before? I have to do it as part of my last year at uni as I didnt do physics at college ( chose mechanics much more interesting!)

anyway its apparently been the same exam for the last 4/5 years but the lecturers give you no help in advance and just give you this equation:

T = 2 * Pi * sqrt(l / g)

T = period (in seconds)
Pi = 3.14...
sqrt = root of ...
l = length of pendulum in m
g = acceleration in m/s^2 (9.81)

I am wondering if anyone has done this experiment but working out G rather than t? if so what would the formula be rearranged? I have found 2 through some googling :

1. g = l/(t/tpi)^2
2. g = 4pi^2L/T^2

Sorry if this is in the wrong section please move if it is

 

[tiny-tim]

good morning, donniemateno!

T = 2 * Pi * sqrt(l / g)

square this equation, then re-arrange it …

what do you get? ​

 

[donniemateno]

Quote by donniemateno
T = 2 * Pi * sqrt(l / g)
square this equation, then re-arrange it …
what do you get?

g = sqrt (2*pi*l )/ T?

 

[tiny-tim]

hi donniemateno!

why aren't there more squares there? ​

 

[donniemateno]

g = sqrt (2*pi*l )/ T^2

I think

Im really not very good at rearranging formulas

I understand the concept of taking one from one side to the other through division but get lost when sqreroots are involved

 

[donniemateno]

a square roots becomes a ^2 so does that mean:

g =(2*pi*l)^2/ T^2

 

[tiny-tim]

ok, then do it one step at a time

first, square T = 2 *π* √(l / g) without any rearranging …

what do you get? ​

 

[donniemateno]

first, square T = 2 *π* √(l / g) without any rearranging

I'm going to say

T^2=2*pi*(l/g)?

 

[tiny-tim]

T² correct

(l/g) correct

 

[donniemateno]

is the next step to divide by 2 pi? if so would that be :

T^2 / 2*pi = (l/g)?

 

[tiny-tim]

whoa!

go back … your 2 *π was not correct …

you needed to square it! ​

 

[donniemateno]

would pi become 4 pi?

 

[tiny-tim]

yup!

T = 2 *π* √(l / g)

becomes

T² = 4 *π²* (l / g)

(you see how you have to square each term separately?)​

ok, now get g on the left and T² on the right

 

[donniemateno]

so next if i divide by g to get

T2 / g = (4 *π2* (l / g)) / g

then divide by t^2 to move it over giving me

g = (4pi*l)/T^2

 

[tiny-tim]

so next if i divide by g to get

T2 / g = (4 *π2* (l / g)) / g

divide by g??

 

[donniemateno]

would it become

t^2*g = 4pi^2*l

then

g = 4pi*l / T^2?

 

[tiny-tim]

(you mean g = 4pi²*l / T² )

yes!
​