Question

A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 23.6° with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is 53.0 kg, and the coefficient of kinetic friction between the skis and the snow is 0.132. Calculate the magnitude of the force that the tow bar exerts on the skier A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 23.6° with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is 53.0 kg, and the coefficient of kinetic friction between the skis and the snow is 0.132. Calculate the magnitude of the force that the tow bar exerts on the skier @Mathematics

Answer 1

A skier is pulled up a slope at a constant velocity by a tow bar. The slope is inclined at 31.0° with respect to the horizontal. The force applied to the skier by the tow bar is parallel to the slope. The skier's mass is 49.9 kg, and the coefficient of kinetic friction between the skis and the snow is 0.232. Find the magnitude of the force that the tow bar exerts on the skier."

The only "complication" here is the slope. The skier's mass is 49.9 kg so his/her weight is 49.9*9.81= 489 N. That's "straight down". Draw a picture and analyise the right triangle formed to see that the "normal force" on the slope is 489(cos(31))= 419.6 Newtons and so the friction force is 0.232(419.6)= 97.3 N. We also need to note that the component of weight parallel to the slope is 489(sin(31))= 251.8 N. The towbar has to equal the sum of those in order to move the skier at constant speed.