# Air resistance in pendulum experiment

1. ### ViresArcanum

3
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.

2. ### Volcano

126
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.

3. ### llauren84

44
How do you calculate the cross section?

Last edited: Apr 28, 2009
4. ### llauren84

44
What is the K?

5. ### Volcano

126
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.

6. ### llauren84

44
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.

7. ### Volcano

126
Don't forget, use little angles(less then 10 degree). This is for both simple pendilum condition and required for less velocity(air resistance).

8. ### llauren84

44
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?

9. ### Volcano

126
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.