An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= x^2+2 #. How much work would it take to move the object over #x in [2, 5], where x is in meters?

1 Answer
P dilip_k
Mar 5, 2016

#=2250 J#

Explanation:

work done against the frictional force
W #=int_2^5u_k(x)mg*dx#
#=int_2^5(x^2+2)*5*10*dx# (Given mass m = 5kg and taking g #10ms^-2#)
#=50int_2^5(x^2+2)dx#
#=50[x^3/3+2x]_2^5#
#=50[(5^3/3+2*5)-(2^3/3+2*2)]#
#=50(117/3+6)#
#=50(135/3)50*45=2250 J#
Here
#{kg*ms^-2*m=N*m=J]#

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