# Solving For Rolling Friction in Bike Tires

• grv413
In summary: This is a problem with static friction - it dominates when the materials are hard but molecular friction becomes dominant when the materials are soft.
grv413

## Homework Statement

Two bicycle tires are set rolling with the same initial speed of 3.60m/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 a distance of 18.0m ; the other is at 105 psi and goes a distance of 92.6m . Assume that the net horizontal force is due to rolling friction only and take the free-fall acceleration to be g = 9.80m/s^2.

What is the coefficient of rolling friction μr for the tire under low pressure?

## Homework Equations

The equations I used are:

1) F=m*a (This would apply to the force in the x direction)
2) (FV)^2= (IV)^2 + 2*(a)*(d)
3) Ff = μ*Fn
4) Fn= m*g

## The Attempt at a Solution

I solved for the acceleration in the x direction using equation 2.
(FV)^2= (IV)^2 + 2*(a)*(d)
(1.8)^2 = (3.6)^2 + 2*(a)*(18)
a= -0.27

So I then plugged this into equations 1 and 3.
F=m*a= μ*Fn
m*a=μ*m*g
m cancels
μ=a/g, so μ=-0.27/-9.8=0.276

I know μ is supposed to be positive, so that is why I made acceleration in the equation negative. I don't quite know where I am going wrong with this work. Any help would be greatly appreciated.

Last edited:
You want to draw a diagram of the forces. Crux here is that ##\vec a## (hence ##\vec F##) and ##\vec d## point in opposite directions.
In other words: once you established a positive x-direction (18 m, 3.6 m/s) it follows that ## |\vec F| = - \mu |\vec F_N|## -- friction force is always opposite to moving force/moving direction

Rolling friction is the resistive force that slows down the motion of a rolling ball or wheel. This type of friction is typically a combination of several friction forces at the point of contact between the wheel and the ground or other surface.

When the materials are both hard, static friction and molecular friction slow down the rolling. When the wheel or tire is soft, its distortion slows down the motion. When the other surface is soft, the plowing effect is a major force in slowing the motion.

Because of the various factors, the coefficient of rolling friction is usually determined experimentally.

Took you a while to post ...
Do these experimenters make their results public somewhere accessible ?
I see a trend towards fatter tyres for trekking bicycles and always thought narrow and hard was better than wide and soft.

## 1. What is rolling friction in bike tires?

Rolling friction is the force that opposes the motion of a bike tire as it rolls on a surface. It is caused by the deformation of the tire and the surface it is rolling on.

## 2. How does rolling friction affect a bike's performance?

Rolling friction can significantly impact a bike's performance by slowing it down and requiring more energy to maintain speed. This can also affect the handling and stability of the bike.

## 3. How is rolling friction calculated?

Rolling friction can be calculated using the formula: F = μN, where F is the rolling friction force, μ is the coefficient of rolling friction, and N is the normal force between the tire and the surface.

## 4. How can rolling friction be reduced in bike tires?

Rolling friction can be reduced by using tires with lower rolling resistance, keeping tires properly inflated, and using smoother and more durable surfaces to ride on.

## 5. Can different types of tire treads affect rolling friction?

Yes, different types of tire treads can have varying levels of rolling resistance and can affect the overall rolling friction of a bike tire. Generally, smoother treads have lower rolling resistance compared to more aggressive treads.

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