As soon as the weather dips below 65 degrees I look forward to my favorite time of year... winter. With winter comes the holidays and most importantly, skiing. Now, being from Syracuse, NY I realize that the skiing here is pretty sub-par, so I look to inspiration via youtube. The most impressive skiing in my opinion is helicopter skiing, where people are simply dropped on the top of the mountain and ski down. Who would have thought this could relate to physics?
Forces in x direction
Forces in y direction
μ of kinetic friction of waxed skis on snow is 0.1
mass of a person is 65 kg.
To find acceleration of skier:
FFr = -μFn = -(0.1) (65 kg) (9.8 m/s2) = -63.7 N
Σ F (y direction) = 0
Σ F (x direction) = FFr + Fg
= -63.7 N + mg sin(20.0) = 154 N
F= (65 kg)(acceleration)
154 N = 65a a= 2.37 m/(s*s)
At Last Frontier in British Columbia, Canada, the average run height is 900 meters.
To find potential energy at the top of the mountain:
PE = mgh
PE = (65 kg)(9.8 m/(s*s))(900. m)
PE = 573300 J --> 573 kJ