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 = 0.55 (static friction) and µk = 0.29 (kinetic friction). The total mass of the bike and biker is 85.0 kg. She is seated so that the normal force the road exerts on her front tire is 1/5 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

Total mass of the biker m = 85 kg coefficient of friction = 0.29 When the biker racing up the hill then by applying Newton's law                         ma = mgcos - mgsin --------------------------------------------------------------------------------------- Therefore the acceleration of the biker is                            a = gcos - gsin -                                                            = g [cos - sin]                               = (9.8 m/s2)[ (0.29)cos9.2 - sin9.2]                               = 1.24 m/s2  

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