# Air resistance in pendulum experiment

by ViresArcanum
Tags: experiment, pendulum, resistance
 P: 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. thanks for your help!
 P: 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.
 P: 44 How do you calculate the cross section?
P: 44

## Air resistance in pendulum experiment

What is the K?
 P: 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_(p...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.
 P: 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.
 P: 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).
 P: 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?
 P: 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.

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