I'm working on a physics project where I aim to demonstrate how different surfaces impact the velocity and acceleration of an RC car due to friction. How can I calculate the coefficient of friction and the force of friction for this experiment?
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1$\begingroup$ A rolling object is not stopped by friction. It is stopped by rolling resistance. Please clarify what you mean. $\endgroup$– Vincent ThackerCommented Jun 13 at 16:28
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2 Answers
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One of the way out to calculate co-efficient of static friction ($\mu_{s}$) is using inclined planes of various angles, you can use a wooden planck and place a carpet above it, and vary the angle as needed.
Considering car to have a mass 'm', 
The equations of motion from the free body diagram can be given as: \begin{equation} N = mgcos\theta \end{equation}
\begin{equation} mgsin\theta - f = ma \end{equation}
where f = $\mu_{s}$N = $\mu_{s}mgcos\theta$
Starting with a small angle $\theta$, the car just begins to move at some specific angle (let's call it $\theta_{\text{moving}}$). The car remains at rest up until this angle, meaning the acceleration is zero. At $\theta_{\text{moving}}$, the car starts to move, indicating a non-zero acceleration. Therefore, for the limiting case: \begin{equation} mgsin\theta_{moving} \geq \mu_{s}mgcos\theta_{moving} \end{equation} \begin{equation} sin\theta_{moving} \geq \mu_{s}cos\theta_{moving} \end{equation} \begin{equation} \mu_{s} \leq tan\theta_{moving} \end{equation}
From this analysis, it is clear that the coefficient of static friction ($\mu_s$) is independent of the car's mass and instead depends on the materials in contact, such as the tire material and the surface material of the inclined plane.
This approach highlights how the static friction coefficient is a material-dependent property and can be effectively determined using the tangent of the angle at which the car just starts to move.
Note: Out of curiosity, you can check how the coefficient of static friction ($\mu_s$) varies on oiling the surface.
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1$\begingroup$ This is just wrong. For example, for a wheel rolling without slipping downslope, the friction is $(mg\sin\alpha)/3$ and not $mg\sin\alpha$. The formula $mg\sin\alpha$ only works when the object has no angular accelerating parts, such as a block sliding downslope. Your analysis is only valid for sliding and not rolling. $\endgroup$ Commented Jun 14 at 13:30
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1$\begingroup$ Rightly said ! I do agree that mgsin$\alpha$ works only for sliding and not considering the rolling into action. But, nowhere in my analysis I nowhere have asked to turn on the car, I have mentioned clearly to just place the car on planck and see for what angle it moves. The question is intending to know about co-efficient of friction and frictional force between the tyre and the carpet. I have given my analysis for static friction co-efficient and static friction force. If the car has geared motors, mostly they slide unless hey are powered. So, I don't agree on you saying it's wrong :-) $\endgroup$ Commented Jun 15 at 9:08
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One way to measure the coefficient of static friction is to place the car on a slope - with the wheels fixed so that the car cannot roll - and gradually increase the angle of the slope. If the car begins to slip when the slope is at an angle $\alpha$ to the horizontal the the coefficient of static friction is $\tan \alpha$.
One way to measure the coefficient of kinetic friction is to attach a force gauge such as a spring balance to the rear of the car and gradually increase the power of the car's engine until its wheels slip. The coefficient of kinetic friction is the reading on the force gauge when the car's wheels begin to slip divided by the car's weight.
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$\begingroup$ This is incorrect. A car is not a flat surface. $\endgroup$ Commented Jun 13 at 17:15
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1$\begingroup$ @VincentThacker If you are hinting at rolling resistance then we can assume that an RC car has solid wheels, in which case rolling resistance will be negligible compared to the frictional forces that we are measuring. If you are hinting at something else then your hint needs details or clarity. $\endgroup$ Commented Jun 14 at 6:46
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$\begingroup$ This is again incorrect. An unpowered rolling wheel on a level surface has zero friction; only rolling resistance. So your first paragraph is incorrect. $\endgroup$ Commented Jun 14 at 8:53
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1$\begingroup$ @VincentThacker The questioner does not ask about the effect of rolling resistance on a coasting car;. They do not even mention rolling resistance. They ask about measuring friction between the wheel and the road surface because they are investigating an accelerating car. I am not going to respond to any further comments from you. $\endgroup$ Commented Jun 14 at 9:25
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$\begingroup$ I know that. I am simply pointing out that your first paragraph is incorrect for a rolling object. For example, for a wheel rolling without slipping downslope, the friction is $(mg\sin\alpha)/3$ and not $mg\sin\alpha$. The formula $mg\sin\alpha$ only works when the object has no angular accelerating parts, such as a block sliding downslope. Your analysis is only valid for sliding and not rolling. $\endgroup$ Commented Jun 14 at 13:31