Question

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?

Answer 1

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.