An object with a mass of $6 k g$ $6 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = 1 + cot x$ $u_k(x)= 1+cotx$ . How much work would it take to move the object over #x in [(pi)/4, (7pi)/8], 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 $u_{k} (x) = 1 + cot x$ $u_k(x)= 1+cotx$ . How much work would it take to move the object over #x in [(pi)/4, (7pi)/8], where x is in meters?

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Answer 1 · 2017-07-21T14:28:36

The work is $= 79.4 J$ $=79.4J$

Explanation:

We need

$\int cot x d x = ln | sin (x) | + C$ $intcotxdx=ln|sin(x)|+C$

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 $m = 6 k g$ $m=6kg$

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

$= 6 (1 + cot x) g N$ $=6(1+cotx)g N$

The work done is

$W = 6 g \int_{\frac{1}{4} π}^{\frac{7}{8} π} (1 + cot x) d x$ $W=6gint_(1/4pi)^(7/8pi)(1+cotx)dx$

$= 6 g \cdot {[x + ln | sin (x) |]}_{\frac{1}{4} π}^{\frac{7}{8} π}$ $=6g*[x+ln|sin(x)|]_(1/4pi)^(7/8pi)$

$= 6 g ((\frac{7}{8} π + ln ∣ ∣ ∣ sin (\frac{7}{8} π) ∣ ∣ ∣)) - (\frac{1}{4} π + ln ∣ ∣ ∣ sin (\frac{1}{4} π) ∣ ∣ ∣))$ $=6g((7/8pi+ln|sin(7/8pi)|))-(1/4pi+ln|sin(1/4pi)|))$

$= 6 g (\frac{5}{8} π - 0.614)$ $=6g(5/8pi-0.614)$

$= 6 g (1.35)$ $=6g(1.35)$

$= 79.4 J$ $=79.4J$

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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 $u_{k} (x) = 1 + cot x$ $u_k(x)= 1+cotx$ . How much work would it take to move the object over #x in [(pi)/4, (7pi)/8], where x is in meters?

1 Answer

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)=1+cotxu_k(x)= 1+cotx . How much work would it take to move the object over #x in [(pi)/4, (7pi)/8], 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 $u_{k} (x) = 1 + cot x$ $u_k(x)= 1+cotx$ . How much work would it take to move the object over #x in [(pi)/4, (7pi)/8], where x is in meters?