Why Is My Calculated 'g' Value Incorrect When Using the Pendulum Equation?

[Danni11111]

Homework Statement

Hi,

I was given a coursework where I have to find the value of the acceleration due to gravity by recording different pendulum lengths & their time period.

here is my data:

Pendulum Length (cm) Time Period (10 swings) (s)

80 8.97
70 8.45
60 7.84
50 7.32
40 6.50

However, every time I used the pendulum equation, I ended up with 'g' having a value around 40, when it is mean to be about 9.81.

I've tried for hours to work out where the flaw in my workings is, but I just can't find it. I've tried converting the cm to m, etc.

Homework Equations

T = 2π * √(L/g)

g = 4π² L / T²

Where T = time period & L = length of pendulum

The Attempt at a Solution

One example of my workings:

T = 0.897
L = 0.8

g = 4π² L / T²

g = 39.478 * 0.8 / 0.897²

g = 39.252


I'm very sure my data isn't wrong either.



Thanks in advance! :)

 

[rock.freak667]

well you see that T²=4π²*L/g = (4π²/g)L

so if you plot T² against L, you will get a straight line passing through the origin whose gradient is 4π²/g.
So plot your graph and get the gradient from it.

 

[Danni11111]

I already plotted it for T squared against L, only problem is, that gradient was ~1.005. That meant that g had to be around 4π2- which is ~39.

Does this mean that it is definitely the data that is wrong and not any of my workings?

I can't help thinking that a second per swing for a pendulum with a length of 80 cm seems reasonably accurate though...

 

[rock.freak667]

I already plotted it for T squared against L, only problem is, that gradient was ~1.005. That meant that g had to be around 4π2- which is ~39.

Does this mean that it is definitely the data that is wrong and not any of my workings?

I can't help thinking that a second per swing for a pendulum with a length of 80 cm seems seasonably accurate though...

For your period, did you divide by 10 to get the time for one period before plotting?

 

[Danni11111]

Yeah- that graph gave me a gradient of ~0.01 :(

 

[rock.freak667]

Yeah- that graph gave me a gradient of ~0.01 :(

I am not too sure why it is not working out, normally your gradient should be around 4. The most I can say is that your measurement of the times are off, but you said they are correct.

EDIT: When you were swinging the pendulum by what angle did you displace the pendulum by each time?

 

[Danni11111]

I'll just have to redo the experiment then- I must have done something awfully wrong :P

thanks for the help!

edit- erm, I didn't do it by an angle, I displaced the pendulum by 20cm from the center for each pendulum length- is that the problem?

 

[diazona]

I doubt that that's the reason your data didn't work out. But it would definitely be better to displace the pendulum by the same angle each time.

Just to check when you were timing swings, you did count a complete back-and-forth cycle as only one swing, right? If not (i.e. if you measured each "swing" only from one maximum displacement to the other), that would almost explain the error in your result.

 

[vela]

I'd guess you didn't measure the period, which is the time for the pendulum to go through one complete cycle, but rather the time for the pendulum to go from one side to the other, so your times are off by a factor of 2, which will cause your estimate of g to be 4 times too large.

 

[Danni11111]

Yep- that's it. I counted each swing as a time period, instead of a swing & back.

I'm changing my excel sheet now.

Thank you so much :)