An object with a mass of $7 k g$ $7 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 4 + sec x$ $u_k(x)= 4+secx$ . How much work would it take to move the object over #x in [(pi)/8, (5pi)/12], where x is in meters?

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An object with a mass of $7 k g$ $7 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 4 + sec x$ $u_k(x)= 4+secx$ . How much work would it take to move the object over #x in [(pi)/8, (5pi)/12], where x is in meters?

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Answer 1 · 2016-02-15T23:05:25

$W ≅ 5, 288 J$ $W~=5,288J$

Explanation:

$W = \int_{\frac{π}{8}}^{\frac{5 π}{12}} u_{k} (x) \cdot d x = \int_{\frac{π}{8}}^{\frac{5 π}{12}} (4 + sec x) \cdot d x$ $W=int _(pi/8) ^ ((5pi)/12) u_k(x)* d x=int _(pi/8) ^ ((5pi)/12) (4+sec x)* d x$
$W = {[4 x + l n (sec x + tan x)]}_{\frac{π}{8}}^{\frac{5 π}{12}}$ $W=[4x+ l n(sec x+tan x)] _(pi/8) ^ ((5pi)/12)$
$W = [\frac{20 π}{12} + l n (\frac{sec (5 π)}{12} + \frac{tan (5 π)}{12})] - [\frac{4 π}{8} + l n (\frac{sec (π)}{8} + \frac{tan (π)}{8})]$ $W=[(20pi)/12 +l n(sec (5pi)/12+tan (5pi)/12)]-[(4pi)/8+l n(sec (pi)/8+tan (pi)/8)]$
$W = [\frac{5 π}{3} + l n (3, 864 + 3, 732)] - [\frac{π}{2} + l n (1, 082 + 0, 414)]$ $W=[(5pi)/3+l n(3,864+3,732)]-[pi/2+l n(1,082+0,414)]$
$W = [\frac{5 π}{3} + l n (7, 596)] - [\frac{π}{2} + l n (1.496)]$ $W=[(5pi)/3+ l n (7,596) ]-[pi/2+l n(1.496)]$
$W = [\frac{5 π}{3} + 2, 028] - [\frac{π}{2} + 0, 403]$ $W=[(5pi)/3+2,028]-[pi/2+0,403]$
$W = [7, 261] - [1, 973]$ $W=[7,261]-[1,973]$
$W ≅ 5, 288 J$ $W~=5,288J$

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An object with a mass of $7 k g$ $7 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 4 + sec x$ $u_k(x)= 4+secx$ . How much work would it take to move the object over #x in [(pi)/8, (5pi)/12], where x is in meters?

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Explanation:

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An object with a mass of 7kg7 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=4+secxu_k(x)= 4+secx . How much work would it take to move the object over #x in [(pi)/8, (5pi)/12], where x is in meters?

1 Answer

Explanation:

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An object with a mass of $7 k g$ $7 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 4 + sec x$ $u_k(x)= 4+secx$ . How much work would it take to move the object over #x in [(pi)/8, (5pi)/12], where x is in meters?