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, (5pi)/12], 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, (5pi)/12], where x is in meters?

1 Answer

Impact of this question

1470 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-20T18:05:34

The work is $= 141.9 J$ $=141.9J$

Explanation:

$Reminder :$ $"Reminder : "$

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

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 coefficient of kinetic friction is $μ_{k} = (5 + tan (x))$ $mu_k=(5+tan(x))$

The normal force is $N = m g$ $N=mg$

The mass of the object is $m = 4 k g$ $m=4kg$

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

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

The work done is

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

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

$= 4 g (\frac{25}{12} π - ln (cos (\frac{5}{12} π))) - (\frac{5}{4} π - ln (cos (\frac{1}{4} π)))$ $=4g(25/12pi-ln(cos(5/12pi)))-(5/4pi-ln(cos(1/4pi)))$

$= 4 g (3.62)$ $=4g(3.62)$

$= 141.9 J$ $=141.9J$

Science

Math

Humanities

... and beyond

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, (5pi)/12], where x is in meters?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

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, (5pi)/12], where x is in meters?

1 Answer

Explanation:

Related questions

Impact of this 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, (5pi)/12], where x is in meters?