- #1

marsten

- 15

- 1

## Homework Statement

A girl, with the mass

*m*, slides down an icy slope at the time

*t*

_{1}=

*τ*. The slope is inclined at 30° below horizontal. The coefficient of kinetic friction between the girl and icy slope is

*μ*

_{k}. The girl notices that she can slide down the slope significantly faster if she sits on a toboggan. The time to slide down on a toboggan (which also has the mass

*m*) proves to be

*t*=½τ. The friction between the toboggan and icy slope can be assumed to be negligible. Determine

_{2}*μ*

_{k}.## Homework Equations

[itex]mgsin\alpha-f_k=ma_{x}[/itex]

[itex]n=mgcos\alpha[/itex]

[itex]f_{k}=μ_{k}n=μ_{k}mgcos\alpha[/itex]

## The Attempt at a Solution

I did a free-body diagram of the girl on toboggan.

Then I tried to solve

*a*with the equations above and got

_{x}*a*since the kinetic friction between the toboggan and surface is negligible.

_{x}=4,9 m/s^{2}Not sure what to do next or if I'm doing wrong from the beginning?

Thanks for any help!

/Marcus from Sweden