Miscalculated Physics?

Question

Physics Phrustration...?
A 67.9kg skier coasts up a snow-covered hill that makes an angle of 27.7o with the horizontal. The initial speed of the skier is 8.54m/s. After coasting a distance of 1.94m up the slope, the speed of the skier is 3.15m/s. Calculate the work done by the kinetic frictional force that acts on the skis.

You are on the right track. Two things remove energy from the skier: frictional force and change in potential energy due to elevation change. The elevation change as you said is ∆h = S*sin(T) where T is the angle of the slope. The energy change from this is m*g*∆h. His starting energy is .5*m*v0^2 where v0 is the starting velocity. The ending energy is .5*m*Vf^2.

The relation is:

end energy - start energy = ∆potential energy + friction energy.

my equation comes out to...

used change PE = mg(hf - hi)
to get 600.07

336.87 - 2476.03 = 600.07 + frictional force

I get -2739 as an answer, but it is still wrong.

Answer 1

Ok, remember conservation of energy:

∆E must equal 0.

Assume starting PE = 0, so the only energy in the beginning is the starting KE.
KE = 2476.03

At the end, you have your final KE, the change in potential energy, and the energy that went to friction. Thus, the initial KE must equal the final KE + PE + Frictional Energy, because all the energy must be accounted for. Try to avoid using a negative value of energy wherever possible.

KE = KEf + ∆PE + FE
2476.03 = 336.87 + 600.07 + FE
FE = 2476.03 = 336.87 + 600.07 = 936.94.