An object with a mass of #1 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 3x^2+x+2 #. How much work would it take to move the object over #x in [1, 3], where x is in meters?

1 Answer
Feb 18, 2016

Answer:

#W=335,54J#

Explanation:

#F_f=u_k*N#
#F_f=" Friction force"#
#"N:Normal force to the contacting surfaces" #
#N=m*g " m:mass of object, g:acceleration of gravity"#
#F_f=u_k*m*g#
#W=int_1^3 F_f*d x#
#W:"work doing by Friction force"#
#W=int_1^3 u_k*m*g*d x#
#W=mg int_1^3 (3x^2+x+2)d x#
#W=mg[3*1/3x^3+1/2x^2+2x ]_1^3+C#
#W=1*9,81[x^3+1/2x^2+2x]_1^3 +C#
#u_k(0)=2 ; then C=2#
#W=9,81([27+4,5+6]-[1+0,5+2])+2#
#W=9,81(37,5-3,5)+2#
#W=9,81*34+2#
#W=335,54J#