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/4, (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/4, (3pi)/4], where x is in meters?

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Answer 1 · 2017-12-22T09:02:21

The work is $= 288.1 J$ $=288.1J$

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 $N = m g$ $N=mg$

The mass is $m = 6 k g$ $m=6kg$

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

$= 6 \cdot (2 + csc x) g$ $=6*(2+cscx)g$

The work done is

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

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

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

$= 6 g (\cdot 4.9)$ $=6g(*4.9)$

$= 288.1 J$ $=288.1J$

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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/4, (3pi)/4], where x is in meters?

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Explanation:

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An object with a mass of 6 kg6kg6 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= 2+cscx uk(x)=2+cscxu_k(x)= 2+cscx . How much work would it take to move the object over #x in [pi/4, (3pi)/4], where x is in meters?

1 Answer

Explanation:

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Impact of this question

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/4, (3pi)/4], where x is in meters?