How to Calculate Tension on a Skier's Rope

Write the slope in degrees of the ski slope you want to analyze. According to the Purdue University Ski and Snowboard club, most popular ski slopes offer beginner slopes with a slope from 10 to 25 degrees. For example, write "13 degrees."

Write the mass of the skier in kilograms. It is necessary to use kilograms so that your answer will be in Newtons, the unit students and scientists most often use when measuring force. For example, write "37 kilograms."

Find the product of the skier's mass, the acceleration of gravity in meters per second squared and the cosine of the slope of the ski slope using a scientific calculator. The cosine button on a scientific calculator is typically labeled "COS." The acceleration of gravity typically is 9.80 meters per second squared. For example, 37 x 9.80 x cos(13) = 329.04. This is the downward, or normal, force, in Newtons, exerted on the skier.

Find the product of your answer and the coefficient of kinetic friction between the skier's skis and the surface of the snow. According to Clifford V. Johnson, a useful coefficient of kinetic friction for waxed skis on snow is 0.05. You must use a kinetic and not static friction coefficient because the skier is in motion. For example, 329.04 x 0.05 = 16.452. The frictional force on the skier is 16.452 Newtons.

Find the product of the skier's mass, the acceleration of gravity and the sine of the slope of the ski slope using your calculator. The sine button on a calculator is typically labeled "SIN." For example, 37 x 9.80 x sin(13) = 152.352. The force exerted by the skier's mass parallel to the slope is 152.352 Newtons.

Find the sum of your answer and the frictional force exerted on the skier. For example, 152.352 + 16.452 = 168.80. The tension in the skier's rope is approximately 168.8 Newtons.