# Relating Coefficient of Friction for my Tyre Experiment

• Matt.D
In summary, a person is conducting an experiment to calculate the coefficient of friction for a tyre sample going against concrete. The experiment involves a uniform piece of concrete angled at 30 degrees, with a pulley attached at one end and a weighted tyre sample placed at the other end. The person is trying to determine the coefficient of friction by adding weights until the rubber sample slips, but is unsure how to factor in the angle of the surface and the weight placed on top of the rubber. They have included a diagram of the setup and are seeking advice on how to proceed with the calculations.
Matt.D
Hi all!

How do you calculate the coefficient of friction for a tyre sample going against concrete?

My experiment involves a uniform piece of concrete angled at 30 degrees with a pulley attached at the raised end.
The tyre sample is placed at the end of the concrete slab and is loaded with 1.0kg of weight to keep it in constant contact with the surface.
The tyre sample is connected to a piece of string that runs over the pulley and at is connected at the other end to a 'weight holder', which I continue to add weights to until the rubber sample moves or loses grip.

I've found that the rubber will take 1.3kg of weight before it slips, but how do I translate that to a coefficient of friction?

I've been looking at a number of formulas, but I can't find any that take into account the angle of the surface - 30 degrees, which I'm sure has a direct effect on the experiment.
Also, do I need to take into account the 'load' I've placed on top of the rubber to keep it pressed down, or will this cancel itself out?

I've uploaded a diagram I drew of how the experiment is setup. Please note the downward arrow above the tyre sample is to exagerate the load pressing down onto the surface. The other arrows pointing to the right and downward, next to the pulley, show the direction of force.

Grey = the floor the experiment is taking place
Orange = the concrete (its a garden edging strip, hence the color ; )
Brown = Wood. I've used a wooden block to hold the concrete block in place and a small piece of wood to make a 'mounting block' for the rubber and weight to go on.

Thanks for looking!

Matt

#### Attachments

• myexperiment.JPG
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What your experiment allows you to find is the maximum static friction that the surfaces can support, which relates to the coefficient of static friction by $\mu N = m_2 g$, where N is the normal force pressing the surfaces together and $m_2$ is the mass of the hanging weight. To find the normal force, consider the forces acting on your 1.0 kg mass. (What's the component of its weight normal to the surface?)

It might help you if you drew a freebody diagram for yourself. First label an axis whose origin is at the center of mass and draw the forces acting on the object. You should notice the relation if you know Newtons laws and trig.

If you do the math correctly you get one of the most "elegant" formulas in physics as a result (lots of things cancel leaving a very simple relationship).

Chi Meson makes an important point. Never rush to just "plug in numbers"; always try to work out the physics symbolically as much as possible. Two big benefits of doing this: (1) Things often simplify greatly, thus reducing your source for arithmetic mistakes when you do finally plug in the numbers, and (2) you stand a much better chance of understanding the physics involved instead of getting lost in arithmetic.

## 1. What is the coefficient of friction and why is it important in a tyre experiment?

The coefficient of friction is a measure of the amount of frictional force between two surfaces in contact. In a tyre experiment, it is important because it can help determine the level of grip or traction that the tyre has on the surface it is moving on. This is crucial in understanding the performance and safety of the tyre.

## 2. How is the coefficient of friction measured in a tyre experiment?

The coefficient of friction can be measured by dividing the force needed to move the tyre by the weight of the tyre. This is known as the static coefficient of friction. In a tyre experiment, the dynamic coefficient of friction can also be measured by calculating the ratio of the force needed to keep the tyre in motion to the weight of the tyre.

## 3. What factors can affect the coefficient of friction in a tyre experiment?

Several factors can affect the coefficient of friction in a tyre experiment. These include the type and condition of the surface the tyre is moving on, the weight and design of the tyre, and the speed and direction of movement. Environmental factors such as temperature and humidity can also play a role.

## 4. How can the coefficient of friction be improved in a tyre experiment?

There are several ways to improve the coefficient of friction in a tyre experiment. These include using different types of tyres with varying tread patterns and materials, increasing the weight of the tyre, and choosing a surface with a higher coefficient of friction. Additionally, maintaining proper tyre pressure and avoiding excessive speed can also improve the coefficient of friction.

## 5. What are the potential implications of a high or low coefficient of friction in a tyre experiment?

A high coefficient of friction can result in better grip and traction, leading to improved performance and safety of the tyre. However, it can also result in increased wear and tear on the tyre and potentially decrease fuel efficiency. On the other hand, a low coefficient of friction can lead to poor handling and less control of the vehicle, increasing the risk of accidents. It can also indicate a worn out or improperly inflated tyre.

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