REMARKS The speed found in part (a) is the same as if the woman fell vertically through a distance of 21.9 m. The result of part (b) is negative because the system loses mechanical energy. Friction transforms part of the mechanical energy into thermal energy and mechanical waves, absorbed partly by the system and partly by the environment. QUESTION If the slide were not frictionless, would the shape of the slide affect the final answer

The result that you are showing is the conservation of mechanical energy between two points in the upper one, the energy is only potential and the lower one is only kinetic.

In the case of some type of friction, the change in energy between the same points is equal to the work of the friction forces

[tex]W_{fr}[/tex] = ΔEm

[tex]W_{fr}[/tex] = [tex]Em_{f}[/tex] -Em₀

As we can see now there is another quantity and for which the final energy is lower and therefore the final speed would be less than what you found in the case without friction.

[tex]Em_{f}[/tex] =[tex]W_{fr}[/tex] + Em₀

Remember that the work of the rubbing force is negative, let's write the work of the rubbing force explicitly, to make it clearer

½ m v² = -fr d + mgh

v = √(-fr d 2/m + 2 gh)

v = √ (2gh - 2fr d/m)

Now it is clear that there is a decrease in the final body speed.

Consequently, if the system has friction, the final result is affected by the loss of energy.