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?
First we will write the information provided
we know that the work done by us to the 5 kg mass is
but in this case there is friction is involved which can be included in the equation by ,
here we need to move the block without acceleration so the applied force must be equal to the kinetic friction .
similarly the work done will also be the same in both the cases so the work done by the frictional force is given by .