An object, previously at rest, slides #8 m# down a ramp, with an incline of #pi/4 #, and then slides horizontally on the floor for another #12 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

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Answer 1 · 2016-04-26T18:30:53

#mu=0,28#

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#"Total Energy for System at the Point of A is:"#

#E_A=m*g*h#

#"where h="8*sin (pi/4)=8*0,707=5,66 m#

#color(green)(E_A=m*g*5,66 J)#

#"This Energy is spent by friction force along the path A,B,C"#

#W_"AB"=color(red)(F_f*bar(AB) " changed heat or any other energy" )#

#W_"AB"=color(red)(mu*m*g*cos(pi/4)*8#

#W_"BC"=color(blue)(F_f*bar(BC)" changed heat or any other energy")#

#W_"BC"=color(blue)(mu*m*g*12)#

#color(green)(cancel(m*g)*5,66=color(red)(mu*cancel(m*g)*0,707*8))+color(blue)(mu*cancel(m*g)*12)#

#5,66=8,49 mu+12 mu#

#20,49 mu=5,66#

#mu=(5,66)/(20,49)#

#mu=0,28#