Calculating air resistance for a cart rolling down a ramp

[Tar123]

Homework Statement

How do you determine the impacts of cross sectional area and velocity on air resistance when you roll a cart down a ramp?

Relevant Equations

Air resistance=kv^2

I'm not sure if any other equations are needed

I am doing a physics lab where we are supposed to calculate air resistance and find the impacts of velocity and cross sectional area on air resistance. For the experiment, we rolled a cart down a ramp and measured data using Pasco Capstone software. When rolling the cart down the ramp, we increased cross sectional area of the cart to see its impact on air resistance. We also did a different trial where we increased velocity by increasing the angle of the ramp to see its impact on air resistance. In the software, we created d-t, v-t, and a-t graphs and fitted them with equations based on the lines observed (linear for a-t, quadratic for v-t, and cubic for d-t). I know increasing the cross sectional area and velocity both increase air resistance and I have all the data, but I'm not sure where to go from here/what calculations to do in order to prove this. Any tips/explanations/sample calculations would be appreciated. Thank you!

 

[BvU]

Hello @Tar123 , !

I'm not sure if any other equations are needed

Well, you will need relationships that feature the observed data and link them to the desired parameters. I don't see area A and I don't see angle $\alpha$ anywhere...

Area A, for example, does appear here

 

[Tar123]

Hello @Tar123 , !

Well, you will need relationships that feature the observed data and link them to the desired parameters. I don't see area A and I don't see angle $\alpha$ anywhere...

Area A, for example, does appear here

The original area was 30cm^2 and we doubled, tripled, and quadrupled this to see the effects on air resistance. For the angles, we started at 4 degrees.

 

[BvU]

The original area was 30cm^2 and we doubled, tripled, and quadrupled this to see the effects on air resistance. For the angles, we started at 4 degrees.

fitted them with equations based on the lines observed (linear for a-t, quadratic for v-t, and cubic for d-t)

That's data, not relationships (equations). What did you do with the fit results ?

 

[Tar123]

That's data, not relationships (equations). What did you do with the fit results ?

Nothing yet. That's where I'm having trouble. I need to analyze the graphs to determine a velocity to use in the equation for air resistance but I can't figure out how to do that. I'm just looking for a bit of help getting started and getting on the right track. I can send a picture of the graphs and fit results if that would help. Also, thank you for the help.

 

[haruspex]

First thing to consider is the problem of separating the influences. Does your experiment that changes the cross section affect the velocity too? Does changing the ramp angle alter the effect of the cross section?
What do the answers to those questions tell you about how to proceed?

fitted them with equations based on the lines observed (linear for a-t, quadratic for v-t, and cubic for d-t)

Are you saying that you observed those shapes for the different parameters, or did you assume those should be the relationships?
Please post your plots.

 

[Tar123]

First thing to consider is the problem of separating the influences. Does your experiment that changes the cross section affect the velocity too? Does changing the ramp angle alter the effect of the cross section?
What do the answers to those questions tell you about how to proceed?

Are you saying that you observed those shapes for the different parameters, or did you assume those should be the relationships?
Please post your plots.

Thank you for the help! Changing one shouldn't affect the other I don't think.

I'm very confused about the graphs and what they mean.

 

[haruspex]

Changing one shouldn't affect the other I don't think.

You don’t think changing the cross section will change the velocity?

Your table only seems to show how displacement etc. vary with time elapsed during a single trial, so profile is constant.
What you need to study is how the velocity affects drag. Of displacement, velocity and acceleration, which is the clearest indicator of drag? So what should you plot against what?
(And use a scale which makes full use of the y axis.)

 

[BvU]

I'm very confused about the graphs and what they mean.

Are you familiar with the SUVAT equations ?

Re fit results:

1. What do you expect to find for position as a function of time ?
2. And if that's too complicated: What do you expect to find for position as a function of time in the absence of drag ?
3. Based on 1: why did you do a cubic fit (or was it just following instructions) ?
4. Position is presented in four digits. What is the acccuracy of the observations ?