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?

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Answer 1 · 2016-06-11T10:40:34

Work $W=1973.0bar6" "$ Joules

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.

An object with a mass of 8 kg8 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 5x^2-3x+1 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?