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, (pi)/6], 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, (pi)/6], where x is in meters?

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Answer 1 · 2017-09-06T07:59:26

The work is $= 45.93 J$ $=45.93J$

Explanation:

We need

$\int sec x d x = ln (tan x + sec x) + C$ $intsecxdx=ln(tanx+secx)+C$

The work done is

$W = F \cdot d$ $W=F*d$

The frictional force is

$F_{r} = μ_{k} \cdot N$ $F_r=mu_k*N$

The normal force is $N = m g$ $N=mg$

The mass is $m = 7 k g$ $m=7kg$

$F_{r} = μ_{k} \cdot m g$ $F_r=mu_k*mg$

$= 7 \cdot (4 + sec x) g$ $=7*(4+secx)g$

The work done is

$W = 7 g \int_{\frac{1}{8} π}^{\frac{1}{6} π} (4 + sec x) d x$ $W=7gint_(1/8pi)^(1/6pi)(4+secx)dx$

$= 7 g \cdot {[4 x + ln (tan x + sec x)]}_{\frac{1}{8} π}^{\frac{1}{6} π}$ $=7g*[4x+ln(tanx+secx)]_(1/8pi)^(1/6pi)$

$= 7 g ((\frac{2}{3} π + ln (tan (\frac{π}{6}) + sec (\frac{π}{6})) - (\frac{1}{2} π + ln (tan (\frac{π}{8}) + sec (\frac{π}{8})))$ $=7g((2/3pi+ln(tan(pi/6)+sec(pi/6))-(1/2pi+ln(tan(pi/8)+sec(pi/8)))$

$= 7 g (\frac{1}{6} π + 0.549 - 0.403)$ $=7g(1/6pi+0.549-0.403)$

$= 45.93 J$ $=45.93J$

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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, (pi)/6], where x is in meters?

1 Answer

Explanation:

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An object with a mass of 7 kg7kg7 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 4+secx uk(x)=4+secxu_k(x)= 4+secx . How much work would it take to move the object over #x in [(pi)/8, (pi)/6], 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, (pi)/6], where x is in meters?