An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 1 + 3 csc x$ $u_k(x)= 1+3cscx$ . How much work would it take to move the object over #x in [(pi)/6, (pi)/4], where x is in meters?

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An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 1 + 3 csc x$ $u_k(x)= 1+3cscx$ . How much work would it take to move the object over #x in [(pi)/6, (pi)/4], where x is in meters?

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Answer 1 · 2016-04-01T12:17:42

$w = \int_{\frac{π}{6}}^{\frac{π}{4}} μ_{k} (x) \cdot m \cdot g d x$ $w=int_(pi/6) ^(pi/4)mu_k(x)*m*gdx$
$w = m g \int_{\frac{π}{6}}^{\frac{π}{4}} (1 + 3 csc x) d x$ $w=mgint_(pi/6) ^(pi/4)(1+3cscx)dx$
$w = m g \int_{\frac{π}{6}}^{\frac{π}{4}} d x + 3 m g \int_{\frac{π}{6}}^{\frac{π}{4}} csc x d x$ $w=mgint_(pi/6) ^(pi/4)dx+3mgint_(pi/6) ^(pi/4)cscxdx$

$= m g \int_{\frac{π}{6}}^{\frac{π}{4}} d x + 3 m g \int_{\frac{π}{6}}^{\frac{π}{4}} csc x d x$ $=mgint_(pi/6) ^(pi/4)dx+3mgint_(pi/6) ^(pi/4)cscxdx$

#= mg(pi/4-pi/6)-3mgln(csc(pi/4)+cot(pi/4)-ln(csc(pi/6)+cot(pi/6)))#
pl put m=6kg
$g = 9.8 m s^{- 2}$ $g=9.8ms^-2$
and values from trigonometrical table and calculate
$w = 6 \times 9.8 \cdot \frac{π}{12} - 3 \times 6 \times 9.8 \times ln (\frac{\sqrt{2} + 1}{2 + \sqrt{3}}) J$ $w= 6xx9.8*pi/12-3xx6xx9.8xxln((sqrt2+1)/(2+sqrt3))J$

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An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 1 + 3 csc x$ $u_k(x)= 1+3cscx$ . How much work would it take to move the object over #x in [(pi)/6, (pi)/4], where x is in meters?

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An object with a mass of 6kg6 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=1+3cscxu_k(x)= 1+3cscx . How much work would it take to move the object over #x in [(pi)/6, (pi)/4], where x is in meters?

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An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 1 + 3 csc x$ $u_k(x)= 1+3cscx$ . How much work would it take to move the object over #x in [(pi)/6, (pi)/4], where x is in meters?