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)/12, (pi)/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)/12, (pi)/12], where x is in meters?

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Answer 1 · 2017-06-22T08:49:34

The work is $= 180 J$ $=180J$

Explanation:

We need

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

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 $m = 7 k g$ $m=7kg$

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

$= 7 (4 + sec x) g$ $=7(4+secx)g$

The work done is

$W = 7 g \int_{- \frac{1}{12} π}^{\frac{1}{12} π} (4 + sec x) d x$ $W=7gint_(-1/12pi)^(1/12pi)(4+secx)dx$

$= 7 g \cdot {[4 x + ln (tan x + sec x)]}_{- \frac{1}{12} π}^{\frac{1}{12} π}$ $=7g*[4x+ln(tanx+secx)]_(-1/12pi)^(1/12pi)$

$= 7 g ((4 \cdot \frac{1}{12} π + ln (tan (\frac{1}{12} π) + sec (\frac{1}{12} π)) - (- 4 \cdot \frac{1}{12} π + ln (tan (- \frac{1}{12} π) + sec (- \frac{1}{12} π)))$ $=7g((4*1/12pi+ln(tan(1/12pi)+sec(1/12pi))-(-4*1/12pi+ln(tan(-1/12pi)+sec(-1/12pi)))$

$= 7 g (\frac{2}{3} π + 0.265 + 0.265)$ $=7g(2/3pi+0.265+0.265)$

$= 7 g (2.624)$ $=7g(2.624)$

$= 180 J$ $=180J$

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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)/12, (pi)/12], where x is in meters?

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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)/12, (pi)/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)/12, (pi)/12], where x is in meters?