T^2 vs L determining g?

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In summary, the conversation is about a lab where the participants were finding how amplitude, bob mass, and length affect the period T for each time. The question at hand is "From your graph of T^2 vs. L, determine a value for g." The participants discuss their graphs and calculations, trying to figure out how to find g from the given data. Eventually, they determine that the slope of the T^2 vs L graph should be equal to 4pi^2/g, and using this equation, they calculate a predicted value for g. After considering the uncertainty and calculating the percent error, they confirm that their predicted value is close to the expected value of 981 cm/s^2.
  • #1
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Okay this is the last question of the lab and I don't get it
Basically its a lab where we find how amplitude, bob mass, and length affects the period T for each time.

Our finding was that length affects the period a lot. I did a bunch of graphs and tables and answered all the questions but don't know how I derive this


the question is "From your graph of T^2 vs. L
determine a value for g."

T here is the period in seconds and L is the length of the string in cm. Now I do have to graph and it looks pretty normal to me.


The slope is 0.03900 and the r is 0.9947
now I don't think this would help much at all
(unless its r-slope haha...)

I have to find g from this graph and calculate the percent of error
I know how to calculate the percent of error but I don't know how I can find g from this graph


the points are for x which is length

50
60
70
80
90
100

and for T^2 i have

2.2831
2.4586
2.89
3.3562
3.7288



My first guess was i need to find an equation for this relationship and then
use the formula 4pi^2/g x L = T^2 but I don't know what to do?

plug in what for L? someone please help!
 
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  • #2
8parks11 said:
Okay this is the last question of the lab and I don't get it
Basically its a lab where we find how amplitude, bob mass, and length affects the period T for each time.

Our finding was that length affects the period a lot. I did a bunch of graphs and tables and answered all the questions but don't know how I derive this


the question is "From your graph of T^2 vs. L
determine a value for g."

T here is the period in seconds and L is the length of the string in cm. Now I do have to graph and it looks pretty normal to me.


The slope is 0.03900 and the r is 0.9947
now I don't think this would help much at all
(unless its r-slope haha...)

I have to find g from this graph and calculate the percent of error
I know how to calculate the percent of error but I don't know how I can find g from this graph


the points are for x which is length

50
60
70
80
90
100

and for T^2 i have

2.2831
2.4586
2.89
3.3562
3.7288



My first guess was i need to find an equation for this relationship and then
use the formula 4pi^2/g x L = T^2 but I don't know what to do?

plug in what for L? someone please help!
As you said, the equation is [itex] T^2 = {4 \pi2 \over g} L [/itex] . So if you plot T^2 vs L, you should get a straight line. The slope of this line will be equal to what?
 
  • #3
wait I don't get it a lot.
so for the x-axis I get all the L (from 50~100) and then just leave it.
for the y, I should use [itex] T^2 = {4 \pi2 \over g} L [/itex] and then subsitute all the L from the x data. that would gimme T^2
but I don't think this is right because I'm getting 4.028 as my slope
 
  • #4
8parks11 said:
wait I don't get it a lot.
so for the x-axis I get all the L (from 50~100) and then just leave it.
for the y, I should use [itex] T^2 = {4 \pi2 \over g} L [/itex] and then subsitute all the L from the x data. that would gimme T^2
but I don't think this is right because I'm getting 4.028 as my slope
:confused: You measured the period for different values of L, right? Just plot your measured values of T^2 versus L. Then use theory to determine what the slope should be equal to. Theory will give you a relation between the slope of this graph and the value of g. Once you measure the slope on your graph you will be able to determine g from your data.
 
  • #5
ok so the slope of my line of T^2 vs L is 0.0390.

since 4pi^2/g=slope g should be 4pi^2/slope...


so the predicted g is 4pi^2/ 0.0390

and this gives me 1012.267... what is wrong?
 
Last edited:
  • #6
8parks11 said:
ok so the slope of my line of T^2 vs L is 0.0390.

since 4pi^2/g=slope g should be 4pi^2/slope...


so the predicted g is 4pi^2/ 0.0390

and this gives me 1012.267... what is wrong?
What is the uncertainty? this is not far from the expected value of about 981 cm/s^2!
 
  • #7
yes haha thanks i forgot that its in cm haha

just to confirm, tthe % error would be 1- (980/1012.267) right?
 
Last edited:

1. What is the relationship between T^2 and L in determining g?

The relationship between T^2 (period squared) and L (length) in determining g (acceleration due to gravity) is described by the equation g = 4π^2L/T^2. This equation is known as the law of gravitation and was first discovered by Isaac Newton.

2. How is the value of g calculated using T^2 and L?

The value of g can be calculated by rearranging the equation g = 4π^2L/T^2 to g = 4π^2L/T^2. This means that if the length and period of an object are known, the value of g can be determined by plugging these values into the equation.

3. Why is T^2 measured instead of T when determining g?

T^2 is measured instead of T (period) because it eliminates the error caused by the reaction time of the experimenter. By squaring the period, the effects of reaction time are cancelled out, resulting in a more accurate measurement of g.

4. What factors can affect the accuracy of using T^2 and L to determine g?

There are several factors that can affect the accuracy of using T^2 and L to determine g. These include air resistance, changes in temperature, and the accuracy of the timing device used to measure the period. It is important to control for these factors in order to obtain a more precise measurement of g.

5. How is the value of g affected by changes in T^2 and L?

The value of g is directly proportional to T^2 and inversely proportional to L. This means that if the period of an object increases, the value of g will also increase. Similarly, if the length of the object increases, the value of g will decrease. This relationship is described by the equation g = 4π^2L/T^2.

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