Frictional Force in Rock Climbing

Rock climbing is one of my favorite activities, and I wanted to explore how physics is used throughout different aspects of climbing. 

Many aspects of climbing technique and of climbing gear are designed to increase frictional force. For example, climbers put chalk on their hands to decrease sweat and increase the coefficient of static friction of their hands. Climbing shoes are made of soft rubber designed to mold to the features in the rock, which also increases the coefficient of static friction because more parts of the shoes are in contact with a rougher surface. This increased friction helps the climber to stay on the wall because there is more force opposing the motion of them slipping off. 

Besides the aspects of the climber that are directly in contact with the rock, the rope systems are also designed to increase friction so that if a climber falls, they fall slower and a shorter distance. According to the work-energy principle, the more work done by nonconservative forces—friction in this case—the less energy that gets converted from the initial gravitational potential energy into kinetic energy and into final gravitational potential energy. 

Below is a picture of a common anchor used at the top of climb to hold the rope. Using two carabiners in the anchor allows the rope to stay in place if one of the carabiners fails, and it also doubles the frictional force of the carabiners on the rope. This frictional force opposes the motion of the climber if they fall and, therefore, opposes the force of gravity; an increase in this upward frictional force means that the climber falls less far.

In addition to using equipment that increases frictional force, the belayer, the person responsible for taking slack out of the rope and catching the climber’s falls, can position their end of the rope at an angle that can increase the y-component of the frictional force of the belay device on the rope. This y-component is important because it is parallel to the force of gravity. If the climber falls, and the rope attached to them moves downward, the end of the rope that the belayer is holding will move upward. The frictional force in the belay setup opposes this upward motion. Positioning the belayer’s end of the rope with as small of an angle between the belay device and the rope allows the y-component of the frictional force from the belay device on the rope to be as large as possible so that the belayer’s end of the rope moves upward as little as possible. This increase in frictional force of the belay device on the rope increases the work done by friction for the entire system, thereby decreasing the velocity of the climber and the climber's change in gravitational potential energy.