Calculate how work done by nonconservative forces on skater?

Question

A 100kg inline skater does 4000J of nonconservative work by pushing against the ground with his skates. In addition, friction does -1000J of non conservative work on the skate. The skates initilal speed is 2.50m/s and his final speed is 1m/s. Has the skater gone uphill, downhill or remained on a flat level. Calculate the change in height of the skater.

Answer 1

Well, the net work (energy) done by skater is 3000J (probably ... although the 1000J might be interpreted as per skate!!)

You can calculate initial and final kinectic energy (Ti and Tf)

If net work is Q, and change in potential energy is deltaU, then

Ti + Q = Tf + deltaU

You know Ti, Tf (1/2 mv^2) and Q -- so solve for deltaU.

Since in this case the work was positive, but speed (kinectic energy) decreased, then the skater must have gone uphill (i.e. increased potential energy).  Once you find deltaU, this is also equal to m*g*h (m = mass, g=9.8m/s^2, h=height in meters)