VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko The skier is going down this slope at constant speed which means the component of gravity directed down the slope 'Fgx' is equal in magnitude to the friction force that's opposing the velocity. The friction force is going up the slope. And so that's what we say here. And 'Fgx' is 'mgsine(theta)' because this 'Fgx' is the opposite leg of this gravity triangle. The force of friction is 'mu k ' times normal force and the normal force equals the component of gravity perpendicular to the slope, which is 'mg cos(theta)' and it's using cosine because it's the adjacent leg of this triangle. Then we substitute into here from both of these lines so we have that the force of friction is 'mg cos(theta)' times the coefficient of kinetic friction. And then we have that 'Fgx' is 'mg sine(theta)' so that's what we we write here and then we divide both sides by 'mg' and they just disappear, which is nice and we also divide both sides by 'cos(theta)' and you get this line here that the coefficient of kinetic friction is 'sine(theta)' divided by 'cos(theta)' and you need to memorize that 'sine(theta)' over 'cos(theta)' is always 'tangent(theta)' and that means the coefficient of kinetic friction is tangent of the slope angle, which is twelve degrees and that makes 'mu k' equal to 0.21.