Friction / inclined plane question

AI Thread Summary
The problem involves a child sliding down a 28-degree incline, where her final speed is half of what it would be on a frictionless slide. The equations of motion are set up using free body diagrams, with gravity split into its x and y components. The normal force and friction force are calculated, leading to the equation m*g*sin(28) - μk*(m*g*cos(28)) = m*acceleration(x). A hint suggests considering the work done by friction as the child moves down the slide. The goal is to find the coefficient of kinetic friction (μk) between the slide and the child.
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I am having trouble setting up the following problem:

A child slides down a slide with a 28 degree incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

I drew an FBD. I split gravity up into it's X and Y components. I know that Force friction = Mu k * Force normal. Fg(x) = m*g*sin(28). Fg(y) = m*g*cos(28)

Force normal - m*g*cos(28) = m*acceleration(x) = 0

m*g*sin(28) - Mu k * ( m*g*cos(28) ) = m*acceleration(x)

Any ideas?
 
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HINT: How much work does the frictional force do on the slide as it traverses the slope?
 
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