An object, previously at rest, slides #9 m# down a ramp, with an incline of #(pi)/6 #, and then slides horizontally on the floor for another #24 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer
Feb 20, 2016

Answer:

#k~=0,142#

Explanation:

#pi/6=30^o#
#E_p=m*g*h " Potential Energy of Object"#
#W_1=k*m*g*cos 30*9 #
#"Lost energy because friction on inclined plane"#
#E_p-W_1": energy when object on ground"#
#E_p_W_1=m*g*h-k*m*g*cos 30^o*9#
#W_2=k*m*g*24 " lost energy on the floor"#
#k*cancel(m*g)*24=cancel(m*g)*h-k*cancel(m*g)*cos 30^o*9#
#24*k=h-9*k*cos 30^o#
#"using "cos 30^o=0,866 ;h=9*sin30=4,5 m#
#24*k=4,5-9*k*0,866#
#24*k+7,794*k=4,5#
#31,794*k=4,5#
#k=(4,5)/(31,794)#
#k~=0,142#