An object, previously at rest, slides #3 m# down a ramp, with an incline of #(3pi)/8 #, and then slides horizontally on the floor for another #5 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~=0,45#

Explanation:

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#"Total Energy at The Point of A: "E_p=m*g*3*sin alpha#
#"The Work doing by The Friction Force along AC:"#
#W_(AC)=3.u_k*m*g*cos alpha#
#"Total Energy at The Point of C:"#
#W_C=E_p-W_(AC)#
#W_C=m*g*3*sin alpha-3.u_k*m*g*cos alpha#
#"The Work doing by Friction Force along CD:"#
#W_(CD)=u_k*m*g*5#
#3 cancel(m. g.) sin alpha -3.u_k. cancel(m. g.) cos alpha=5. u_k .cancel(m .g)#
#3.sin alpha-3.u_k.cos alpha=5.u_k#
#2,772-u_k.1,148=5.u_k#
#2,772=5.u_k+1,148.u_k#
#2,772=6,148.u_k#
#u_k~=0,45#