# Designing an experiment to establish a relationship between speed and air resistance

Synxervious
Hello. I'm a physics student in high school, and I'm trying to design an experiment. I've encountered a small setback, though.

## Homework Statement

Investigating the relationship between the speed of a table tennis ball and the force of air resistance exerted upon it.

## Homework Equations

v^2=u^2+2as, v=u+at, f=ma, s=ut+1/2at^2

## The Attempt at a Solution

The purpose of this lab is to investigate the relationship between the speed of a table tennis ball and the force of air resistance exerted upon it. In order to perform this investigation, I will vary the speed of a table tennis ball under two circumstances, the first of which in a vacuum (the control group), where air resistance does not apply, and the second of which in a non-vacuum, where air resistance does apply.
I will vary the speed of the table tennis ball by using a nichrome spring compressed to a certain length. I will calculate the force that will be generated using the formula F=kx. For both the control and the non-control group, for each trial performed, I will record the time taken for the table tennis ball to travel a fixed distance, s from the starting point thrice to obtain an average using a stopwatch. I expect to find a discrepancy in the time taken for the table tennis ball to travel to the fixed distance, s from the starting point between the control group and the non-control group due to air resistance in the non-control group. I expect the ball from the non-control group to take a longer time to reach s by virtue of the force of air resistance acting against the acceleration. From this discrepancy in time, I will calculate the force that is exerted upon the table tennis ball by air resistance.

Sadly, I do not know how to. Will someone please teach me how to using the basic equations of motion please. Thanks. Please tell me what to substitute into a in the equation kx-ma= F of air resistance.

a) If an object travels a certain distance over a certain time period, I can obtain the speed by dividing the distance traveled by the time taken. Can I divide the speed by the same amount of time to obtain the acceleration of the object, assuming the initial speed is 0?
b) if there is anything else that I should add to my experiment.

N-Gin

I'm not sure how exactly you want do find the relationship between the force and the speed of a tennis ball. I don't know if this will help, but I have a suggestion. The simplest method would probably be putting the ball on the instrument which can precisely measure the force exerted upon it and then try to move the whole thing with a certain speed (that you also need to measure). That way you can directly measure both the speed and the force and see how are they related. Best way is to draw a diagram, where you can roughly see the dependence.

I don't know if you are familiar with some data analysis methods (such as linear regression) which can also give you the error (to see how sure you can be in your conclusion).

You can also do it by assuming the dependence, then predicting the results of measurements theoretically and then see if (and how much) the measurements match the theoretical model.

Hope this helps!