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

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

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Answer 1 · 2018-06-25T06:13:57

The work is $= 359.5 J$ $=359.5J$

Explanation:

$Reminder :$ $"Reminder : "$

$\int tan x d x = ln | (cos (x)) | + C$ $inttanxdx=ln|(cos(x))|+C$

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 coefficient of kinetic friction is $μ_{k} = (5 + tan (x))$ $mu_k=(5+tan(x))$

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

The mass of the object is $m = 4 k g$ $m=4kg$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

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

$= 4 \cdot (5 + tan (x)) g$ $=4*(5+tan(x))g$

The work done is

$W = 4 g \int_{- \frac{1}{12} π}^{\frac{5}{12} π} (5 + tan (x)) d x$ $W=4gint_(-1/12pi)^(5/12pi)(5+tan(x))dx$

$= 4 g \cdot {[5 x + ln | (cos (x)) |]}_{- \frac{1}{12} π}^{\frac{5}{12} π}$ $=4g*[5x+ln|(cos(x))|]_(-1/12pi)^(5/12pi)$

$= 4 g (\frac{25}{12} π + ln (cos (\frac{5}{12} π))) - (- \frac{5}{12} π + ln (cos (- \frac{1}{12} π))$ $=4g(25/12pi+ln(cos(5/12pi)))-(-5/12pi+ln(cos(-1/12pi))$

$= 4 g (9.17)$ $=4g(9.17)$

$= 359.5 J$ $=359.5J$

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

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Explanation:

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An object with a mass of 4 kg4kg4 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 5+tanx uk(x)=5+tanxu_k(x)= 5+tanx . How much work would it take to move the object over #x in [(-pi)/12, (5pi)/12], where x is in meters?

1 Answer

Explanation:

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