# Friction and Newton's Laws

## Homework Statement

A child slides down a slide with a 34 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.

## Homework Equations

$$\Sigma$$F = ma
$$\Sigma$$FR=$$\mu$$FN

## The Attempt at a Solution

set x-axis along incline.
Got FN=mgcos$$\theta$$ and gsin$$\theta$$-gtan$$\theta$$cos$$\theta$$=a
Now I don't know what to do. I have a = 4.92 m/s2, but I feel I can't proceed without $$\Delta$$x or t....

ehild
Homework Helper
Check your equation for a. Now it is equivalent to a=0.

Try to apply the Work-Energy theorem.

ehild

Last edited:
HallsofIvy
Let the coefficient of kinetic friction by $\mu$. Now you can calculate the component of the child's weight normal to the slide from the given angle and the length of the slide assuming height h and the given angle. The work done by the friction force is the coefficent of friction times the friction force times the length of the slide and that must be equal to 3mgh/4.