How Does Friction Affect Spring Compression on an Incline?

[bignasty]

A 2.0 kg package is released on a 53.1◦
incline, 4.0 m from a long spring with force
constant 120 N/m that is attached at the
bottom of the incline. The coefficient of
friction between the package and the incline
are µs=0.40 and µk=0.20. The mass of the
spring is negligible.
a. Show that the maximum
compression of the spring is 1.06m.
b. The package rebounds back up the
incline. Show that the package
comes to rest at a distance 1.32 m
below its initial position.

I'm not even quite sure where to begin on part a, and I don't even understand what they are asking for on part b. For part a, it seems like it might be a conservation of energy problem, but I'm not sure how to set up the equation. Any hints would be greatly appreciated!

Big Nasty

 

[thenewbosco]

As with any conservation of energy problem the following equation will be very useful:

$$-W_{friction} = \Delta U + \Delta K$$ where U is potential energy and K is kinetic energy

you will have to calculate the work done by friction (force of friction times distance), over the entire distance it travels, and the change in vertical distance(done using the angle), the amount of compression in the spring will also appear in the potential energy of the spring. One good thing about energy though is that the velocity, thus kinetic energy, can be ignored in this since both initial and final kinetic energies are zero.

If you need some more help just ask.

P.s. I worked it out and got 1.06m as the answer for a)

 

[bignasty]

Thanks

Thanks for the hint, I tried it and I got the answer to match what was given in the problem. I appreciate it!



Big Nasty