Air resistance in pendulum experiment

[ViresArcanum]

hey guys, I've been experimenting with a pendulum and while doing the error discussion for my experiments i got stuck with the air resistance involved...
I've used the formula to find the force applied by the air resistance to the pendulum and ended up with F=2,76*10^-5 *v^2 . (v= velocity of the pendulum).

Basically i just want to estimate how much of an error percentage of my results air resistance has caused, but i don't have much of an idea how to calculate this percentage.
thanks for your help!

 

[Volcano]

I suppose you mean drag force.

F = K S v^2

K: Constant
S: widest cross-section
v: velocity

The velocity is changing time by time. Yo may not use one velocity to calculate it. In fact the velocity of body has,

V = Vm Sin(wt)

where V: sudden, Vm: max, w=2(pi)f and t: time

But if we use a average worth, i would put my money to :) ,

V = Vm/sqrt(2)

this is better than others.

F = K S ( Vm/sqrt(2) )

this is a suggestion. Maybe there is a better solution.

 

[llauren84]

How do you calculate the cross section?

 

[llauren84]

What is the K?

 

[Volcano]

Sorry, assumed you know. Known air resistance formula,

F= - 1/2 p v^2 A C

p: density of the fluid
v: speed of the object relative to the fluid
A: reference area
C: drag coefficient

You can look at below link
(http://en.wikipedia.org/wiki/Drag_(physics)#Parasitic_drag)

Mostly you don't calculate the effective cross sectional area. It is "reference area" in last equation. For a spherical body, widest cross section area is a circle which has the same radius of sphere. And forget K :) use the latest formula.

Warning, I have no idea about finding(calculating) the effect of air resistance for pendulum. I am not sure about certainty of above(first) suggestion. Just an approach. I wanted to help you to find a good average drag force. So I find a good average velocity to use in formula.

If you use a long string, even max. velocity will be more little. So drag force(air resistance) effect will be much less. But calculation is not so easy.

 

[llauren84]

So, basically calculating it is not even worth it if it is so small. So that probably wouldn't have an effect on our experiment. Thanks for the help.

 

[Volcano]

Don't forget, use little angles(less then 10 degree). This is for both simple pendilum condition and required for less velocity(air resistance).

 

[llauren84]

But how come, even when we used 45 degrees, the period, according to the photogate was still T=2π √(L/g)=1.22?

L was 37cm=.37m
g=9.8m/s2

My data was like this:

Theta in degrees, T
05, 1.194
10, 1.196
15, 1.201
20, 1.203
25, 1.209
30, 1.215
35, 1.223
40, 1.238
45, 1.241

I am guessing that the ball was steel...So is wind resistance even a factor there? Is it just my error?

 

[Volcano]

Look at here http://en.wikipedia.org/wiki/Pendulum you will see another period equation for larger amplitudes.

Maybe because of bigger air friction :) larger degrees are not much big as expected. But look closer, T is already growing. Learn the exact acceleration of gravity and compare with yours then see which one is closer to formula.