An object with a mass of #8 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 5x^2-3x+1 #. How much work would it take to move the object over #x in [2, 3], where x is in meters?

1 Answer

Answer:

Work #W=1973.0bar6" "#Joules

Explanation:

Work #dW=F*dx#

#F=mu_k*N#

#F=mu_k*m*g#

#dW=mu_k*m*g*dx#

#W=int_2^3 mu_k*m*g*dx#

#W=int_2^3 (5x^2-3x+1)*(8)(9.8)dx#

#W=78.4 int_2^3 (5x^2-3x+1)dx#

#W=78.4 [ (5x^3)/3-(3x^2)/2+x)]_2^3#

#W=78.4[45-27/2+3-(40/3-6+2)]#

#W=1973.0bar6#

God bless....I hope the explanation is useful.