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

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Answer 1 · 2016-06-11T10:40:34

Work $W = 1973.0 ¯ 6$ $W=1973.0bar6" "$ Joules

Work $d W = F \cdot d x$ $dW=F*dx$

$F = μ_{k} \cdot N$ $F=mu_k*N$

$F = μ_{k} \cdot m \cdot g$ $F=mu_k*m*g$

$d W = μ_{k} \cdot m \cdot g \cdot d x$ $dW=mu_k*m*g*dx$

$W = \int_{2}^{3} μ_{k} \cdot m \cdot g \cdot d x$ $W=int_2^3 mu_k*m*g*dx$

$W = \int_{2}^{3} (5 x^{2} - 3 x + 1) \cdot (8) (9.8) d x$ $W=int_2^3 (5x^2-3x+1)*(8)(9.8)dx$

$W = 78.4 \int_{2}^{3} (5 x^{2} - 3 x + 1) d x$ $W=78.4 int_2^3 (5x^2-3x+1)dx$

$W = 78.4 [\frac{5 x^{3}}{3} - \frac{3 x^{2}}{2} + x)]_{2}^{3}$ $W=78.4 [ (5x^3)/3-(3x^2)/2+x)]_2^3$

$W = 78.4 [45 - \frac{27}{2} + 3 - (\frac{40}{3} - 6 + 2)]$ $W=78.4[45-27/2+3-(40/3-6+2)]$

$W = 1973.0 ¯ 6$ $W=1973.0bar6$

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An object with a mass of 8kg8 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=5x2−3x+1u_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?