Air resistance in pendulum experiment

• ViresArcanum
In summary, the pendulum swings back and forth with a period of 2π√(L/g), where L is the length of the pendulum. The heavier the ball, the longer the period.

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.

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.

How do you calculate the cross section?

Last edited:
What is the K?

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.

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.

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

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?

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.

1. What is air resistance?

Air resistance is a force that acts against the motion of an object through the air. It is caused by the collision of air molecules with the surface of the object, which creates drag and slows down the object's motion.

2. How does air resistance affect a pendulum experiment?

Air resistance can affect a pendulum experiment by altering the motion of the pendulum. It can reduce the amplitude (height) of the swing and increase the time it takes for the pendulum to complete one full swing. This can result in inaccurate measurements and affect the overall results of the experiment.

3. Can air resistance be eliminated in a pendulum experiment?

No, it is not possible to completely eliminate air resistance in a pendulum experiment. However, it can be minimized by conducting the experiment in a vacuum or using a pendulum with a streamlined design to reduce the surface area exposed to air resistance.

4. How can air resistance be accounted for in a pendulum experiment?

Air resistance can be accounted for by measuring the amplitude and time period of the pendulum's swing in the presence of air resistance, and then subtracting these values from the measurements taken in the experiment. This allows for a more accurate calculation of the effects of air resistance on the pendulum's motion.

5. Does air resistance affect all pendulums the same way?

No, the effect of air resistance on a pendulum can vary depending on factors such as the weight, size, and design of the pendulum. A heavier and more streamlined pendulum will experience less air resistance compared to a lighter and more complex pendulum.

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