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 [(-5pi)/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 [(-5pi)/12, (5pi)/12], where x is in meters?

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Answer 1 · 2017-08-12T12:19:20

The work is $= 513.1 J$ $=513.1J$

Explanation:

We need

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

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

The mass is $m = 4 k g$ $m=4kg$

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

$= 4 (5 + tan x) g$ $=4(5+tanx)g$

The work done is

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

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

$= 4 g ((5 \cdot \frac{5}{12} π + ln ∣ ∣ ∣ cos (\frac{5}{12} π) ∣ ∣ ∣) - (5 \cdot - \frac{5}{12} π + ln ∣ ∣ ∣ cos (- \frac{5}{12} π) ∣ ∣ ∣))$ $=4g((5*5/12pi+ln|cos(5/12pi)|)-(5*-5/12pi+ln|cos(-5/12pi)|))$

$= 4 g (\frac{50}{12} π + ln ∣ ∣ ∣ cos (\frac{5}{12} π) ∣ ∣ ∣ - ln ∣ ∣ ∣ cos (\frac{5}{12} π) ∣ ∣ ∣)$ $=4g(50/12pi+ln|cos(5/12pi)|-ln|cos(5/12pi)|)$

$= 4 g (\frac{25}{6} π + 0)$ $=4g(25/6pi+0)$

$= 513.1 J$ $=513.1J$

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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 [(-5pi)/12, (5pi)/12], where x is in meters?

1 Answer

Explanation:

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Science

Math

Humanities

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An object with a mass of 4kg4 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=5+tanxu_k(x)= 5+tanx . How much work would it take to move the object over #x in [(-5pi)/12, (5pi)/12], where x is in meters?

1 Answer

Explanation:

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Impact of this question

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 [(-5pi)/12, (5pi)/12], where x is in meters?