An object with a mass of $1 kg$ is pushed along a linear path with a kinetic friction coefficient of $u_k(x)= e^x-1$ . How much work would it take to move the object over #x in [1, 3], where x is in meters?

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Answer 1 · 2018-05-22T12:14:03

The work is $=150.63J$

$"Reminder : "$

$inte^xdx=e^x+C$

The work done is

$W=F*d$

The frictional force is

$F_r=mu_k*N$

The coefficient of kinetic friction is $mu_k=(e^x-1)$

The normal force is $N=mg$

The mass of the object is $m=1kg$

$F_r=mu_k*mg$

$=1*(e^x-1)g$

The work done is

$W=1gint_1^3(e^x-1)dx$

$=1g*[e^x-x]_1^3$

$=1g(e^3-3)-(e-1)$

$=1g(15.37)$

$=150.63J$

An object with a mass of 1 kg1 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, 3], where x is in meters?