Question

A bicyclist is coasting straight down a hill at a constant speed. The mass of the rider and bicycle is 96.0 kg, and the hill is inclined at 17.0° 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?

Answer 1

When coasting down the hill, the force of gravity assists the motion. When climbing the hill at the same constant speed, a force must be applied to overcome gravity. The force can be calculated using the equation Force = mass * 9.8 * sin(angle).

Step-by-step explanation:

When the bicyclist is coasting straight down the hill, the force of gravity acts parallel to the hill, assisting the motion. The force applied to the bicycle in this case is zero, since the bicyclist is only using the force of gravity to move down the hill.

When the bicyclist climbs the hill at the same constant speed, the force applied to the bicycle must overcome the force of gravity acting against the motion.

To calculate this force, we need to determine the component of the force of gravity parallel to the hill. This can be calculated using the equation:

Force = mass * 9.8 * sin(angle)

where mass is the mass of the rider and bicycle (96.0 kg) and angle is the inclination of the hill (17.0°).