Newtons Laws applied at an incline including a spring and friction

Dear Helpers,

I'm sitting since ours in front of a task and trying to solve it.

Attached you find a picture to the problem.

Given:

θ=28°

μs=0.4

μk=0.3

k=30N/m

m1=1kg

m2=2kg

x0=0

x1=1m --> Spring is stretched



The question is:

Does m2 move up or downwards?





First thing I tried to solve it like this: I considered gravitation, friction and the force of the spring.

So I was thinking the following:

F(Spring)=-k*x

F(Object2)=m2*g

F(Object1)=m1*g*sin(28) <-- is this sin(28) correct?

F(Friction)=μk*F(Normal)

What is in this case the normal Force (F(Normal))?



F(Spring) + F(Friction) > F(Object2) + F(Object1) --> moves upwards

F(Spring) + F(Friction) < F(Object2) + F(Object1) --> moves downwards





I do understand, that I need to sum up all the forces an compare them. But is my way correct? Do I forget to consider sth? Maybe somebody is able to help me.



b) Would be "When does m2 touch the table gently?

For task b)

F=-kx^2

h=1m

Thanks in advance

Gio

Attached Images

WP_20140629_003.jpg (73.6 KB)