Calculating Air Drag for Projectiles Lab

[bwong]

Homework Statement

I am unable to calculate air drag for a projectiles lab I am doing.
It involves shooting elastic bands and measuring the distance they travel and compare it to the theoretical distance(with and without friction).
It takes 0.45 seconds for the elastic band to fall and its initial velocity is dependent upon the stretch. I also have measured the mass(0.37grams) and the k value (31 N/m).

Homework Equations

the equation 1/2 ACdrag p v^2 is only valid for teh initial drag force, but since the projectile loses velocity as time increases, how would i calculate the average drag force. (I also do not know the final velocity)

The Attempt at a Solution

I have thought about integrating the graph Fdrag v.s V, however, I do not have the final velocity.

 

[quantumdude]

The average velocity is easy. It's just the change in position divided by the change in time. You'll need to do this for both the horizontal and vertical components of the motion. You can deduce the final velocity as follows. In Calculus I you would have learned that the average value $f_{av}$ of a function $f$ is given as follows.

$$f_{av}=\frac{1}{b-a}\int_a^bf(x)dx$$

Since you know $f_{av}$, as well as the integrand and the lower limit of integration, you can find the upper limit of integration (which in your case will be the final speed).

 

[Moetasim]

As a scientist, my first recommendation would be to gather more accurate and precise data. This could involve using more precise measuring tools, such as a digital scale for the mass measurement, and conducting multiple trials to get a more accurate average distance traveled. Additionally, I would suggest using a more accurate and reliable method for measuring the initial velocity of the elastic band, such as using a high-speed camera or a motion sensor.

Once you have gathered more accurate data, you can use the equations of motion and Newton's laws of motion to calculate the average drag force. This would involve using the initial velocity, mass, and k value to calculate the initial drag force, and then using the equations of motion to calculate the final velocity and the time it takes for the elastic band to fall. From there, you can use the average velocity and the initial and final times to calculate the average drag force.

If you are unable to obtain the final velocity, you could use the average velocity instead. However, keep in mind that this may introduce some error into your calculations. Alternatively, you could also use the slope of the graph of Fdrag vs. V to estimate the final velocity, as long as your data points are accurate and reliable.

Overall, the key to accurately calculating air drag for this projectiles lab is to gather precise and accurate data and then use the appropriate equations and principles of physics to analyze and interpret the data.