An object with a mass of 5 kg is pushed along a linear path with a kinetic friction coefficient of u_k(x)= e^x+x . How much work would it take to move the object over #x in [1, 2], where x is in meters?

2 Answers
May 7, 2017

283.53J

Explanation:

First we will write the information provided
mu_k=e^x+x
M=5 Kg

we know that the work done by us to the 5 kg mass is
W=F_(applied)*ds

but in this case there is friction is involved which can be included in the equation by ,

W=(F_(applied)-f_(k))*dS

here we need to move the block without acceleration so the applied force must be equal to the kinetic friction .
F_(applied)=f_k

similarly the work done will also be the same in both the cases so the work done by the frictional force is given by .

W=f_k*dx=mu_k*N*dx=int_1^2(e^x+x)*m*g*dx=283.53J

May 7, 2017

The work is =302.3J

Explanation:

The work done is

W=F*d

The frictional force is

F_r=mu_k*N

N=mg

F_r=mu_k*mg

=5(e^x+x)g

The work done is

W=5gint_(1)^(2)(e^x+x)dx

=5g*[e^x+x^2/2]_(1)^(2)

=5g((e^2+2)-(e+1/2)))

=5g(9.39-3.22)

=5g*6.17

=302.3J