SOLUTION: A 60 kg skier is pulled by a rope up a frictionless slope that is inclined at an angle of 20 degree with the horizontal. The rope pulls parallel to the slope and has a tension of 2

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A 60 kg skier is pulled by a rope up a frictionless slope that is inclined at an angle of 20 degree with the horizontal. The rope pulls parallel to the slope and has a tension of 2      Log On


   

Question 160954: A 60 kg skier is pulled by a rope up a frictionless slope that is inclined at an angle of 20 degree with the horizontal. The rope pulls parallel to the slope and has a tension of 230N. Calculate the skier's acceleration.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
There is no frictional force acting on the skier but there is a component of gravity acting against the skier.
The force balance, parallel to the slope, would be
T-mgsin%28alpha%29=ma
where T is the tension of the rope and alpha is the angle of incline,
a=%28T-mgsin%28alpha%29%29%2Fm
a=%28230-60%289.8%29sin%2820%29%29%2F60
a=0.48
The skier accelerates at a rate of 0.48 m/s^2.