A sled weighing 200 N rests on a 15° incline, held in place by static friction?

A sled weighing 200 N rests on a 15° incline, held in place by static friction. The coefficient of static friction is 0.5.





c) The sled is now pulled up the incline at constant speed by a child. The child weighs 520 N and pulls on the rope with a constant force of 100 N. The rope makes an angle of 30° with the incline and has negligible weight. What is the magnitude of the kinetic friction force on the sled? (Enter 0 if sled does not move.)


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(d) What is the coefficient of kinetic friction between the sled and the incline? (Enter 0 if sled does not move.)


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(e) What is the magnitude of the force exerted on the child by the incline?


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A sled weighing 200 N rests on a 15° incline, held in place by static friction?
(c)


Ff = 100cos30 ≈ 86.60254 N ≈ 86.6 N


(d)


100cos30 = μ((200)cos15 - 100sin30)) + 200sin15


μ = (100cos30 - 200sin15) / ((200)cos15 - 100sin30))


μ ≈ 0.2433124 ≈ 0.243


(e)


F^2 = (100cos30 + (0.5)(560)sin15)^2 + (560cos15 + (0.50(100)sin30)^2


F^2 ≈ 103,314.13167283 + 320,263.70644949


F^2 ≈ 423,577.83812233


F ≈ 650.8286 N ≈ 651 N