Block and spring collision - work

[zhenyazh]

Hi,
i am preparing for a test and have some problem with the following question.

A moving 2.40 kg block collides with a horizontal spring whose spring constant is 400 N/m.

The block compresses the spring a maximum distance of 5.00 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.450. What is the work done by the spring in bringing the block to rest?

so to find the work done by the spring i should use
w=f*x and in this case since the the force is not constant i should use an integral
of f along the path.
but the result i get is wrong. this i probably because i don't address the friction here.
i just don't know where to push it and i am not sure i should.
if i do the integral until 0.05m that means i implicitly address friction, because if
it were not for it the block would have had a larger trajectory.
can u help?

an image is attached

thanks

 

[sezw]

ok first what you got to do is find the net force the force applied is what is used to move the object but you must think of it as a vector first
force applied is positive whilst ff is negative
to find the force of friction you must find the normal force which is easy because it is on a flat surface so Fn is the opposite of Fg i think what you were doing is doing is work=force applied x displacement you need the force net multiplied by displacement and make sure that you convert the 5cm into meters
after that you should be fine just remember Eps=K9constant) multiplied by delta X delta x is the displacement
do not attempt to solve this question as a scaler solve it as a vector quantity

 

[zhenyazh]

Ok great,
but should it not be an integral?
that is the spring force which is part of net force is changining along with the displacement