An object, previously at rest, slides #4 m# down a ramp, with an incline of #pi/4 #, and then slides horizontally on the floor for another #15 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

1 Answer
Mar 6, 2016

Answer:

#u_k~=0,158#

Explanation:

#"Total Energy of object:"#
#E_p=m*g*4*sqrt2/2" "E_p=m*g*2sqrt2#
#"Work doing by the Friction Force on Ramp"#
#W_f=u_k*m*g*4*sqrt2/2" "W_f=u_k*m*g*2sqrt 2#
#"Total Energy on floor"#
#Delta E=m*g*2sqrt2-u_k*m*g*2sqrt2#
#color(red)(W_f=(u_k*m*g)*15)#
#color(red)"work doing by The Friction Force on Floor"#
#Delta E=cancel(m*g)*2sqrt2-u_k*cancel(m*g)*2sqrt2=color(red)(u_k*cancel(m*g)*15#
#2sqrt2-u_k*2sqrt2=u_k*15#
#2sqrt2=15*u_k+2sqrt2*u_k#
#2,82=15*u_k+2,82*u_k#
#2,82=17,82*u_k#
#u_k=(2,82)/(17,82)#
#u_k~=0,158#