When a bicycle rider is coasting straight down a hill at a constant speed, a few forces are in play. The mass of the rider and bicycle combined is 87.0 kg, and the hill is inclined at 13.0 degrees with respect to the horizontal. Even though the rider seems to be moving downhill effortlessly, several factors are balancing each other out.
First, we need to consider gravity. The force of gravity acts downward, pulling the cyclist toward the Earth. This force can be broken down into two components: one that acts perpendicular to the slope of the hill, and another that acts parallel to it. The component acting parallel to the slope is what propels the cyclist downward. However, since the speed is constant, this gravitational force must be balanced by another force.
The opposing force in this scenario is air resistance, also known as drag. As the bicyclist moves down the hill, air resistance works against the motion, which can be significant at higher speeds. Since the rider is coasting at a constant speed, the net force acting on them must be zero. This means that the downhill force due to gravity is precisely equal to the force of air resistance.
This balance of forces demonstrates Newton’s first law of motion, which states that an object in motion will stay in motion with a constant velocity unless acted upon by a net external force. In this case, while the bicyclist is in motion down the hill, the forces acting on them are balanced, allowing for constant speed.
Thus, although it might seem effortless, the physics of coasting involves a careful interplay of gravitational pull and aerodynamic drag, maintaining that constant speed as the rider descends the incline.