Help on inclined plane and air resistance.

[TexasCow]

Homework Statement

Hey,
As an end of the year easy grade, our physics teacher assigned us a 20 point project in where we design a lab and analyze the data in a power point. I chose to use an inclined plane and a roller cart. My idea was to analyze the effect of a sail (thus creating air resistance) on the acceleration of the cart. So, I had two identical carts, one with no sail, and another with a large piece of cardboard attached to it to create air resistance. I performed trials in which position and velocity were recorded for five seconds.

My questions are:
-How can I analyze air resistance with my method?
-What are useful equations that I can use?
-My teacher mentioned the cross sectional area of my sail; how is this related?

Thank you

*Note: Screen shots of data coming soon.

 

[robertm]

First off I assume you are conducting your experiment indoors with some sort of launch mechanism to ensure accurate results. Secondly you would really need to know how in depth of an analysis you want to go into. But you at least need to know: velocity, acceleration, mass, momentum, force, area of the sail, and I imagine you might want to go into the fluid dynamics of the air being displaced by the sail. Good luck

 

[moshka]

could you draw a diagram of what actually your project is?and tell what year are you are you student of university or are you in high school?

 

[TexasCow]

The data analysis itself does not have to be very indepth at all, I just have to maybe verify some sort of constant and/or equation? I'm a senior in AP Physics by the way.
http://img229.imageshack.us/img229/7817/img019sg9.jpg

In the picture, the motion sensor is at the top of the ramp and it is connected to the laptop that's in the picture.

 

[robertm]

Looks nice, what exactly is the motion sensor measuring? Seams to me you should just do some data plots showing the relation between sail area and velocity/acceleration with the cart sans-sail as a control. Sweet and simple, but a fairly good project; especially if you use some computer software to analyze your data. Btw, are you just going to let the cart hit a barrier to stop? Maybe you should allow the cart room to accelerate to a stop and analyze that data as well...

 

[TexasCow]

The cart stopped at a pillow type barrier. The motion sensor provided me with position and velocity graphs with and sans-sail.

 

[TexasCow]

Well it's due tomorrow and I don't have the program on my computer. So as of right now I've got to do with the graphs of velocity and acceleration, and the area of the sail...any ideas?

 

[robertm]

Well it seems that it is a little too late to make any major changes now, so just be sure to be as exact in your measurements and calculations as you can and by doing so fully explain the behavior of the cart using basic kinematics.

Writing a very exhaustive lab report will definitely have the most help. Be as professional in your language as possible and maybe add a section where you predict the exact motion of the cart beforehand through mathematics, which is what you should have done in the first place, and then compare your predictions with the raw data.

Or you could even do some theoretical situations where you could make the sail very large or very small and predict the effects, or try changing around the atmospheric pressure and predict those effects.

Your experiment is simple in its nature (for your purposes) and that is not necessarily a bad thing; I would rather see a very well done simple experiment than a disastrous cool one. The best of luck tomorrow TexasCow!

 

[TexasCow]

Thanks a lot Robertm. My teacher also suggested using the drag equation F=-bv. How does that relate? I do have the velocity at a certain point but I do not know how to calculate the force at this time. I suppose I could use "ma" but I do not have the mass of my cart.

 

[robertm]

Oh my, you really should weigh your cart! I believe you should Include: Velocity, Acceleration, Kinetic Energy, Potential Energy, Work, Power, Momentum, and prove conservation of energy and momentum. You could add some more values but I think for your purposes this will be enough. Most of these values can be found on paper, but you really need to know the mass of you cart with and without the sail/sails.

And calculating drag is a very applicable option. Drag is a resistance force arising from an object moving through a fluid, as your cart moving through the air. All the same forces are involved as if your cart were a submarine!

Here is a link to the equation as I know it, I believe what you wrote is a shortened version: http://en.wikipedia.org/wiki/Drag_equation

 

[TexasCow]

How would I find the drag coefficient?

 

[robertm]

2F/Apv^2 that being:

two times the force applied to the object by the fluid

divided by

the cross sectional area of the surface (area of the sail should suffice)

times

the density of the fluid

times

the relative velocity of the object squared

 

[robertm]

Knowing the mass of your cart plus the sail, the angle and length of your ramp, the effects G, and negating friction; you can produce what the theoretical instantaneous force should be right before the impact on the pillow. Using your experimental data derive the actual force of the cart with the affects of friction (air resistance). The difference in force will approximate the drag force of air on your cart. Knowing F, you can derive the drag coefficient and apply the drag formula to any theoretical situation involving the cart. And compare your experimental values to your theoretical values.

Don't forget to include all this in your methodology! You should manage to swings some pretty high scores, let me know how it goes!