# Work and energy bicycle question

1. Dec 7, 2003

### templaroftheages

A cyclist and her bicycle have a combined mass of 75 kg. she coasts down a road inclined at 2.0 degrees with the horizontal at 4.0 m/s and coasts down another road inclined at 4.0 degrees at 8.0 m/s. she then holds on to a moving vehicle and coasts on a level road. what power must the vehicle expend to maintain her speed at 3.0 m/s? assume that the force of air resistance is proportional to her speed, and assume that other frictional forces remain constant?
thanks.. if anyone could solve this, it'd be great help

2. Dec 8, 2003

### HallsofIvy

Staff Emeritus
You can calculate the gravitational force from these. Since she is not accelerating, the total friction force must be exactly the same as the gravitational force. You are told that the air resistance is proportional to speed (which you know) and that all other frictional forces remain constant. These two situations give two equations for the two unknowns (coefficient of air resistance and "other frictional forces").

Once you have solved for those, you can put them into the force equation for the level road situation and determine the force necessary to keep her moving at constant speed. Power is work divided by time so: multiply the force by the distance moved in a fixed t and divide by t.