- #1
audrey1203
- 1
- 0
Homework Statement
A child slides down a slide with a 28° incline, and at the bottom her speed is precisely half what it would have been if the slide had been friction-less. Calculate the coefficient of kinetic friction between the slide and the child.
Knowns:
28°
speed=V/2
Homework Equations
##\Sigma F=ma##
##{ F }_{ fr }={ \mu }_{ k }{ F }_{ N }##
##{ v }^{ 2 }={ v }_{ 0 }^{ 2 }+2a(x-{ x }_{ 0 })##
The Attempt at a Solution
##\Sigma { F }_{ y }=ma=0##
##{ F }_{ N }-mgcos\sigma =0##
##{ F }_{ N }=mgcos\sigma##
##{ \Sigma F }_{ x }=ma##
##-{ F }_{ fr }+mgsin\sigma =ma##
##{ F }_{ fr }=\frac { ma-mgsin\sigma }{ -1 } ##
##{ F }_{ fr }=-ma+mgsin\sigma ##
##{ F }_{ fr }={ \mu }_{ k }{ F }_{ N }##
##-ma+mgsin\sigma ={ \mu }_{ k }mgcos\sigma ##
##\frac {-ma+mgsin\sigma }{ mgcos\sigma } ={ \mu }_{ k }##
##\frac { -a+gsin\sigma }{ gcos\sigma } ={ \mu }_{ k }##