# Solving For Rolling Friction in Bike Tires

**1. The problem statement, all variables and given/known data**

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?

**2. Relevant 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

**3. 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.

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