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 $x \in [\frac{π}{12}, \frac{π}{3}]$ $x in [(pi)/12, (pi)/3]$ , 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 $x \in [\frac{π}{12}, \frac{π}{3}]$ $x in [(pi)/12, (pi)/3]$ , where x is in meters?

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Answer 1 · 2017-05-31T08:18:40

The work is $= 179.75 J$ $=179.75J$

Explanation:

The work done is

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

The frictional force is

$F_{r} = μ_{k} \cdot N$ $F_r=mu_k*N$

$N = m g$ $N=mg$

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

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

The work done is

$W = 4 g \int_{\frac{1}{12} π}^{\frac{1}{3} π} (5 + tan x) d x$ $W=4gint_(1/12pi)^(1/3pi)(5+tanx)dx$

$= 4 g \cdot [5 x - ln | cos x |)]_{\frac{1}{12} π}^{\frac{1}{3} π}$ $=4g*[5x-ln|cosx|)]_(1/12pi)^(1/3pi)$

$= 4 g ((\frac{5}{3} π - ln ∣ ∣ ∣ cos (\frac{1}{3} π) ∣ ∣ ∣) - (\frac{5}{12} π - ln ∣ ∣ ∣ cos (\frac{1}{12} π) ∣ ∣ ∣))$ $=4g((5/3pi-ln|cos(1/3pi)|)-(5/12pi-ln|cos(1/12pi)|))$

$= 4 g (\frac{5}{4} π + ln 2 + ln (cos (\frac{1}{12} π))$ $=4g(5/4pi+ln2+ln(cos(1/12pi))$

$= 4 g (\frac{5}{4} π + ln 2 (cos (\frac{1}{12} π)))$ $=4g(5/4pi+ln2(cos(1/12pi)))$

$= 4 g \cdot 4.59 J$ $=4g*4.59J$

$= 179.75 J$ $=179.75J$

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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 $x \in [\frac{π}{12}, \frac{π}{3}]$ $x in [(pi)/12, (pi)/3]$ , where x is in meters?

1 Answer

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, (pi)/3]x∈[π12,π3]x in [(pi)/12, (pi)/3], 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 $x \in [\frac{π}{12}, \frac{π}{3}]$ $x in [(pi)/12, (pi)/3]$ , where x is in meters?