# Rolling Friction-Bicycle Tires

• toxsic
In summary, the low-pressure tire has a coefficient of rolling friction of less than 1.0, while the high-pressure tire has a coefficient of rolling friction of 1.0.
toxsic

## Homework Statement

Two bicycle tires are set rolling with the same initial speed of 3.30 m/s along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes 18.6 m; the other is at 105 psi and goes 93.5 m. Assume that the net horizontal force is due to rolling friction only.
What is the coefficient of rolling friction mu_r for the tire under low pressure?

## The Attempt at a Solution

Honestly, I have no idea where to begin. The professor has never explained anything like it and this is a first. It's on mastering physics and it's well above my head

Do you have a mass for each of the tires?

toxsic said:

## Homework Statement

Two bicycle tires are set rolling with the same initial speed of 3.30 m/s along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes 18.6 m; the other is at 105 psi and goes 93.5 m. Assume that the net horizontal force is due to rolling friction only.
What is the coefficient of rolling friction mu_r for the tire under low pressure?

## The Attempt at a Solution

Honestly, I have no idea where to begin. The professor has never explained anything like it and this is a first. It's on mastering physics and it's well above my head

In my previous post, I asked if you had the mass of the tires (plus wheel, of course) but you can get pretty far without that information. Here's the basic idea: The initial kinetic energy of each tire is going to go into work to overcome friction. That work is equal to the frictional force times the distance. So let's set this up:

Let the coefficient of kinetic friction for the tire inflated to 40 psi be denoted by $$\mu_1$$.

And let the coefficient of kinetic friction for the other tire be denoted by $$\mu_2$$

Then the basic relationship is

$$K.E. = F_f d$$

The frictional force for the first tire is, of course, given by $$F_f = \mu_1 N$$
with a similar equation for the other tire.

That implies that, if we label the distance the tire travels by $$d_1$$

$$K.E. = \mu_1 N d_1$$

for the first tire and a similar relationship for the second tire. We'll assume the two tires have the same mass and we know that they start with the same kinetic energy, so you can either set the two expressions equal to each other (or divide one of the equations by the other). At any rate the K.E and the normal forces cancel out leaving you with the two coefficients of friction and the two distances. You can then express one coefficient of friction in terms of the other.

Got that?

## 1. What is rolling friction?

Rolling friction is the resistance that occurs when an object, such as a bicycle tire, rolls over a surface. It is caused by the deformation of the tire and the surface it is rolling over.

## 2. How does rolling friction affect bicycle tires?

Rolling friction can cause a loss of energy in the form of heat and can also slow down the speed of the bicycle. This can result in the need for more energy to be exerted by the cyclist to maintain the same speed.

## 3. How does tire pressure affect rolling friction?

Tire pressure can greatly affect rolling friction. Higher tire pressure can reduce the surface area of the tire in contact with the ground, resulting in less deformation and therefore less rolling friction. However, if the tire pressure is too high, it can also cause the tire to bounce, increasing rolling friction.

## 4. How do different tire designs affect rolling friction?

The design of the tire can greatly impact rolling friction. Tires with a smooth tread pattern have less rolling friction compared to tires with a more aggressive tread pattern. The type of rubber used in the tire can also affect rolling friction.

## 5. How can rolling friction be reduced in bicycle tires?

Rolling friction can be reduced by using tires with a smooth tread pattern, keeping the tire pressure at the recommended level, and using tires with a high-quality rubber compound. Regularly maintaining and replacing worn tires can also help reduce rolling friction.

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