Skier energy problem A skier of mass m=80 kg starts from rest at point A and ski

Question

Skier energy problem

A skier of mass m=80 kg starts from rest at point A and skis down a hill and en up a smaller hill having radius of curvature R = 25 m. The skier is testing some new Frictionless Skis^TM which are (strangely enough) entirely frictionless. Assume g 10 m/s^2. Find the work (if any) done by the snow on the skier with the Frictionless Skis as she moves from point A to point C. Explain your reasoning. Find the kinetic energy of the skier at point B. Find the speed of the skier at point C. Find the acceleration of the skier (magnitude and direction) at point C. Find the magnitude of the normal force by the hill on the skier at point C.

Explanation / Answer

a) The force exerted by the snow on the skier is always normal to its motion. So, the work done by the snow is zero if it is assumed that frictionless surface.

b) mgh at A = 1/2 * m * vb2 at B

   vb = sqrt (2 * g * h) = 24.25 m/s

c) 1/2 * m * vb2 at B = (mgh + 1/2 * m * vc2) at C

vb2 - 2gh = vc2 => vc = sqrt ( vb2 - 2gh ) = 9.89 m/s

d) acceleration at C = vc2 / R = 3.9 m/s2    , towards center

e) N = mg + m * vc2 / R => N = 1097 N

  

    

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