An object with a mass of $1 k g$ $1 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_{k} (x) = e^{x} - 1$ $u_k(x)= e^x-1$ . How much work would it take to move the object over #x in [1, 2], where x is in meters?

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Answer 1 · 2017-05-02T06:25:09

The work is $= 35.97 J$ $=35.97J$

The work done is

$W = F \cdot d$ $W=F*d$

The frictional force is

$F_{r} = μ_{k} \cdot N$ $F_r=mu_k*N$

$N = m g$ $N=mg$

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

$= 1 (e^{x} - 1) g$ $=1(e^x-1)g$

The work done is

$W = \int_{1}^{2} (e^{x} - 1) g d x$ $W=int_(1)^(2)(e^x-1)gdx$

$= g \int_{1}^{2} (e^{x} - 1) d x$ $=gint_(1)^(2)(e^x-1)dx$

$= g \cdot {[e^{x} - x]}_{1}^{x}$ $=g*[e^x-x]_(1)^(2)$

$= g (e^{2} - 2) - (e - 1))$ $=g(e^2-2)-(e-1))$

$= g (5.39 - 1.72)$ $=g(5.39-1.72)$

$= g \cdot 3.67$ $=g*3.67$

$= 35.97 J$ $=35.97J$

An object with a mass of 1 kg1kg1 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= e^x-1 uk(x)=ex−1u_k(x)= e^x-1 . How much work would it take to move the object over #x in [1, 2], where x is in meters?