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 $x \in [\frac{- 5 π}{12}, \frac{π}{4}]$ $x in [(-5pi)/12, (pi)/4]$ , where x is in meters?

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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 $x \in [\frac{- 5 π}{12}, \frac{π}{4}]$ $x in [(-5pi)/12, (pi)/4]$ , where x is in meters?

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Answer 1 · 2017-05-06T21:13:47

As we know that work $= \int_{x_{1}}^{x_{2}} \to F . - \to d x$ $= int_(x_1)^(x_2) vecF.vec (dx)$
Here $F = 4 \times 10 \times (5 + tan x) = 40 \times (5 + tan x)$ $F=4xx10xx (5+tanx)=40xx(5+tanx)$
$:.W=int_-((5pi)/12)^(pi/4)40(5+ tanx)dx$
$=200xx(pi/4-(-(5pi)/12))+40[lnsec (pi/4)-lnsec (-(5pi)/12)]$
Now simplify it...

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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 $x \in [\frac{- 5 π}{12}, \frac{π}{4}]$ $x in [(-5pi)/12, (pi)/4]$ , where x is in meters?

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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 $x \in [\frac{- 5 π}{12}, \frac{π}{4}]$ $x in [(-5pi)/12, (pi)/4]$ , where x is in meters?