At a winter recreation resort, snow tubers at the bottom of the hill hook their

Question

At a winter recreation resort, snow tubers at the bottom of the hill hook their tubes to a tow rope. A motor pulls the rope so that tubers move at constant velocity to the top of the hill. (Ignore the momentary acceleration of the tuber when he first attaches his tube to the rope.) The coefficient of kinetic friction between the tube and the snow is

k = 0.15.

A boy and his tube with a total weight of 400 N are pulled a distance of 310 m up the 20° incline (see figure below). Consider the Earth, the boy, his tube, and the snow along his path to make up the system. Find the tension in the rope. (Enter the magnitude. The work done by the rope is 5.99 104 J.)
N

Explanation / Answer

Fnet = T - W*sintheta - fk

fk = frictional force = uk*W*costheta

Fnet = T - W*sintheta - uk*W*costheta

from newtons second law Fnet = m*a

since the speed is constant acceleration a = 0

Fnet = 0

T - W*sintheta - uk*W*costheta = 0

T - W*sintheta - uk*W*costheta = 0

T - 400*sin20 - 0.15*400*cos20 = 0

T = 193.2 N

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