An object with a mass of $5 k g$ $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = x e^{x} - x$ $u_k(x)= xe^x-x$ . How much work would it take to move the object over #x in [1, 4], where x is in meters?

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An object with a mass of $5 k g$ $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = x e^{x} - x$ $u_k(x)= xe^x-x$ . How much work would it take to move the object over #x in [1, 4], where x is in meters?

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Answer 1 · 2016-02-12T21:25:12

$W = 147, 15 (3 e^{x} - 7) J$ $W=147,15(3e^x-7)J$

Explanation:

$W = F_{f} \cdot x = N \int_{1}^{4} (x e^{x} - x) x \cdot d x$ $W=F_f*x=N int_1^4(x e^x-x) x*d x$
$W = m g \int_{1}^{4} (x^{2} e^{x} - x^{2}) d x$ $W=m g int_1^4 (x^2 e^x-x^2)d x$
$W = m g ({[e^{x} (x^{2} - 2 x + 2)]}_{1}^{x} - {[\frac{1}{3} x^{3}]}_{1}^{3})$ $W=m g ([e^x(x^2-2 x+2)]_1^4 - [1/3 x^3]_1^4)$
$W = m g (9 e^{x} - 21)$ $W=m g(9e^x-21)$
$W = 5 \cdot 9, 81 (9 e^{x} - 21$ $W=5*9,81(9e^x-21$
$W = 147, 15 (3 e^{x} - 7) J$ $W=147,15(3e^x-7)J$

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An object with a mass of $5 k g$ $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = x e^{x} - x$ $u_k(x)= xe^x-x$ . How much work would it take to move the object over #x in [1, 4], where x is in meters?

1 Answer

Explanation:

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An object with a mass of 5kg5 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=xex−xu_k(x)= xe^x-x . How much work would it take to move the object over #x in [1, 4], where x is in meters?

1 Answer

Explanation:

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An object with a mass of $5 k g$ $5 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = x e^{x} - x$ $u_k(x)= xe^x-x$ . How much work would it take to move the object over #x in [1, 4], where x is in meters?