Weight on a Scale Down an Incline vs. True Weight

[Error]

Weight on a Scale Down an Incline vs. True Weight

Homework Statement

Judy fastened a set of bathroom spring scales to a wedge shaped skate board as shown and coasted freely down a 30 degree slope. The wheels were well oiled and the platform supporting the scales was horizontal. What fraction of her true weight was indicated by the scales?
Why would there need to be a force of friction between Judy and the scales?

Homework Equations

Fg = mg

The Attempt at a Solution

(Pictures in attachments)

Fg = mg
Fg_|_ = mgsin60º

F_N = Fg _|_
F_N = mgsin60º

F_Ny = F_Ncos30º
F_Ny = mgsin60ºcos30º
F_Ny = (3/4)mg

The weight will be 3/4 the true weight. (I think)


I'm not too sure why there will have to be friction between Judy and the scale. Will the scale accelerate downwards and she will slip off if there's no friction? Will the scale read zero?

 

[Doc Al]

Your reasoning (and perhaps your trig) is a bit unclear. Try this: What's the acceleration of the woman?