An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 2 + csc x$ $u_k(x)= 2+cscx$ . How much work would it take to move the object over #x in [pi/12, (3pi)/4], where x is in meters?

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An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 2 + csc x$ $u_k(x)= 2+cscx$ . How much work would it take to move the object over #x in [pi/12, (3pi)/4], where x is in meters?

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Answer 1 · 2017-06-04T07:53:45

The work is $= 417.5 J d$ $=417.5Jd$

Explanation:

We need

$\int csc x d x = ln ∣ ∣ tan (\frac{x}{2}) ∣ ∣ + C$ $intcscxdx=ln|tan(x/2)|+C$

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 $N = m g$ $N=mg$

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

$= 6 (2 + csc x)) g$ $=6(2+cscx))g$

The work done is

$W = 6 g \int_{\frac{1}{12} π}^{\frac{3}{4} π} (2 + csc x) d x$ $W=6gint_(1/12pi)^(3/4pi)(2+cscx)dx$

$= 6 g \cdot {[2 x + ln ∣ ∣ tan (\frac{x}{2}) ∣ ∣]}_{\frac{1}{12} π}^{\frac{3}{4} π}$ $=6g*[2x+ln|tan(x/2)|]_(1/12pi)^(3/4pi)$

$= 6 g ((\frac{3}{2} π + ln ∣ ∣ ∣ tan (\frac{3}{8} π) ∣ ∣ ∣) - (\frac{1}{6} π + ln ∣ ∣ tan (\frac{π}{24}) ∣ ∣)$ $=6g((3/2pi+ln|tan(3/8pi)|)-(1/6pi+ln|tan(pi/24)|)$

$= 6 g (\frac{4}{3} π + 0.88 + 2.027)$ $=6g(4/3pi+0.88+2.027)$

$= 6 g (7.098)$ $=6g(7.098)$

$= 42.6 g J$ $=42.6gJ$

$= 417.5 J$ $=417.5J$

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An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 2 + csc x$ $u_k(x)= 2+cscx$ . How much work would it take to move the object over #x in [pi/12, (3pi)/4], where x is in meters?

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Explanation:

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Math

Humanities

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An object with a mass of 6kg6 kg is pushed along a linear path with a kinetic friction coefficient of uk(x)=2+cscxu_k(x)= 2+cscx . How much work would it take to move the object over #x in [pi/12, (3pi)/4], where x is in meters?

1 Answer

Explanation:

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An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 2 + csc x$ $u_k(x)= 2+cscx$ . How much work would it take to move the object over #x in [pi/12, (3pi)/4], where x is in meters?