Finding the coefficient of kinetic friction on an incline

[Brandon Davidson]

<< Mentor Note -- Two threads on the same subject have been merged >>

I am a junior enrolled in IB Physics at the standard level at my high school. As a part of the curriculum we must perform an Internal Assessment (IA) which involves performing an experiment and performing calculations and it also includes a typed paper.

The format of the question for your experiment is "How does x affect y?" For my experiment I decided to formulate the question; "How do different surfaces at an incline affect the time it takes for an object to roll down the incline?"

For the experiment my independent variable, the surfaces on the incline will be cardboard, carpet, cloth, plastic wrap, and wood. The angle of the incline, the displacement the object rolls down the incline, and the object (a marble) will be kept constant. I plan to ultimately find the coefficient of kinetic friction for each of the surfaces by collecting raw data for time. Then I'll use the equation s=ut+(1/2)at² to find the acceleration of the marble on the different surfaces. Next I would use the acceleration and mass to find Net Force.

This is where I get a little confused. Would I utilize similar triangles and vectors to create the new horizontal component since there is an incline and create the equation [Net Force + (Weight)(sinθ) - friction = ma] ? θ would be the angle of the incline. From there would I simply go on to find the coefficient of kinetic friction by using the coefficient of kinetic friction formula involving normal force and the friction I would have found from my previous equation?

Would there also be a vertical component however since the marble is rolling and not stationary on the incline? I am asking for any help with my confusion I can get as well for any tips regarding anything I may be doing wrong with the setup of the experiment or anything I should change. Thanks.

 

[kuruman]

The equation that you propose, [Net Force + (Weight)(sinθ) - friction = ma], is incorrect. The correct form is Net force = ma and Net force = Weight*sinθ - friction. This equation applies to objects sliding down inclines without rolling. Your marble will most likely roll without slipping. This involves another equation for the time needed to travel a certain distance and will not give you the coefficient of kinetic friction. Also, I think that your proposal does not meet the criteria of the question, "How does x affect y?" From what you have said, "y" is the time required for the marble to roll down the incline. Fair enough, but what is "x"? From the looks of it, it is "carpet, cloth, plastic wrap, and wood". I think the question wants you to use an independent variable that can be quantified, such as length, speed, angle, etc. so that you can make calculations to investigate how close your theoretical model reproduces the measured value of the dependent variable y for a given value of the independent variable x.

 

[Brandon Davidson]

For my advanced level (International Baccalaureate) Physics class we are required to do a large project (Internal Assessment) in which we perform research, conduct an experiment, and write a long paper involving our research, experiment results, and data analysis.

The research question I picked is "How do the different coefficients of kinetic friction on varying surfaces affect the total acceleration of a tennis ball on an incline?" I am stumped on the acceleration portion of my project because the tennis ball on the incline in which I placed different surfaces upon is in rotational motion. We haven't learned this topic and I have a bunch of things I can't grasp.

How would I measure the angular displacement in this scenario? (I already performed the experiment and gathered data on the time it took for the tennis ball to roll down a 4 degree incline for five trials on for each five different surfaces placed atop the incline). Are tangential acceleration and linear acceleration the same in this context? Can I even calculate coefficient of kinetic friction from the data I collected while taking all applicable and relevant calculations into account?

How do I find the tangential velocity to calculate the total acceleration? What is moment of Inertia and should I use rotational energy formulas to further investigate and help better answer my question? Should I change my research question to help fit my experiment better?

As you can see, I'm pretty lost. Any assistance or input would be greatly appreciated.

 

[kuruman]

You may wish to reconsider the scope of your project. A tennis ball on a 4^o incline would roll without slipping. This means that the coefficient of kinetic friction does not come into play. For that to happen the two surfaces in contact must be sliding past each other. If you make the angle steep enough, you will get sliding and rolling at the same time in which case the calculation becomes more involved. However, if it's sliding that you want, why not use just a block of wood? That will also solve your problem of not having been exposed to rotational motion.

Yes, to explain the motion of an object rolling down hill you need to study and understand rotational dynamics which includes moment of inertia and the use of rotational energy formulas. If you must do the rolling experiment, how much time do you have to learn all that you need? Analyzing the motion of the ball and showing theoretically and experimentally that the time it takes to travel a certain distance down the incline is the same regardless of surface, is a result in itself. While you're at it, it turns out that the acceleration down the incline is also independent of the radius of the ball or its mass but demonstrating this is could be iffy because of air resistance. A ping-pong ball will take longer than a steel ball of the same diameter to roll down the incline because it's more difficult for it to push the air out of the way.