**67. ssm A bicyclist is coasting straight down a hill at a constant speed. The combined mass of the rider and bicycle is 80.0 kg, and the hill is inclined at 15.0° with respect to the horizontal. Air resistance opposes the motion of the cyclist. Later, the bicyclist climbs the same hill at the same constant speed. How much force (directed parallel to the hill) must be applied to the bicycle in order for the bicyclist to climb the hill?

Free body diagram on the left is the bicyclist coasting downhill.  The one on the right is the bicyclist climbing the hill.

 

Going down

Since there is no motion in the perpendicular direction of the bicyclist on the hill, there is no acceleration perpendicular.

 

Since the bicyclist is traveling at constant speed down the hill, there is no parallel acceleration.  So we can solve for air resistance.

 

 

Going up

 

 

Still traveling at constant speed.

 

Using what we found for air resistance which is assumed to be same up and downhill.

 

 

 

 

 

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This page last updated on January 11, 2020