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 [(-3pi)/12, (pi)/4], where x is in meters?

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 [(-3pi)/12, (pi)/4], where x is in meters?

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Answer 1 · 2017-10-30T17:55:45

The work is $= 307.9 J$ $=307.9J$

Explanation:

We need

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

$- \frac{3}{12} π = - \frac{1}{4} π$ $-3/12pi=-1/4pi$

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 $m = 4 k g$ $m=4kg$

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

$= 4 \cdot (5 + tan x) g$ $=4*(5+tanx)g$

The acceleration due to gravity is $g = 9.8 m s^{- 2}$ $g=9.8ms^-2$

The work done is

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

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

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

$= 4 g (\frac{5}{2} π))$ $=4g(5/2pi))$

$= 10 g π$ $=10gpi$

$= 307.9 J$ $=307.9J$

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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 [(-3pi)/12, (pi)/4], where x is in meters?

1 Answer

Explanation:

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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 [(-3pi)/12, (pi)/4], 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 [(-3pi)/12, (pi)/4], where x is in meters?