Question

Please help me check my answers to the following physics problems. If they are incorrect, please explain the concept to me so I may correct my mistakes.

1. A 60 kg skate-boarder rolls down an inclined sidewalk at a 370 angle to the horizontal. A constant frictional force of 55 N acts on the skate-boarder in opposition to the motion. What is the skate-boarder's acceleration?
[I got a=4.98 m/s²]

2. A patient needs neck traction, but must have the bed inclined at 300 to avoid fluid in the lungs. The coefficient of static friction between the back of the head and the hospital bed is 0.30. The patient's head weighs 40 N. a. What is the normal force on the head? b. What is the maximum static frictional force on the head? c. What is the maximum allowed tension in the traction cable, assuming maximum frictional force?
I'm stuck on number 2. I got N=3.535 and a = -4.64, but I don't think they are correct

Answer 1

a) Normal force (N) = 40 cos 30 degree N = 34.64 newton b) Max. static frictional force (f) = mu N = 0.30 times 34.64 f_max = 10.39 N c) T_max = 40 sin 30 degree + f_max = 20 + 10.39 T_max = 30.39 N