A biker is racing up a hill in the rain. The hill rises at an angle of 9.2 degre

Question

A biker is racing up a hill in the rain. The hill rises at an angle of 9.2 degrees above the horizontal. The coeffients of friction between her tires and the road are µs = 0.56 (static friction) and µk = 0.26 (kinetic friction). The total mass of the bike and biker is 78.0 kg. She is seated so that the normal force the road exerts on her front tire is 1/3 the normal force the road exerts on her back tire.

What is the maximum acceleration of the bike and biker? Give your answer to three digits in units of m/s2. Do not include the units in your answer.

In this problem, the frictional force on the front wheel is going to be much smaller (by a factor of about 50) than the other forces in the problem, so it can be ignored.

Explanation / Answer

The frictional force on the back tire will be
F=(3/4).56mgcos=(3/4).56(78)(9.8)cos(9.2)

F=316.92

F=ma

316.92=78a

a=4.063m/s2

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