# Newton's Laws applied at an incline including a spring and friction

#### gidoru90

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

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#### gidoru90

Sorry, didn't read the "forum" rules before -.- First time, that I'm using a forum. Is it possible to shift my problem to the correct forum!
I'm sorry.

#### Nathanael

Homework Helper
Sorry, didn't read the "forum" rules before -.- First time, that I'm using a forum. Is it possible to shift my problem to the correct forum!
I'm sorry.
I'm sure someone with the ability will move this thread once they see it.

About your question, there is a third possibility, that the object doesn't move at all. We should rule out this possibility first.

For the system not to move, what must be the case?

#### jtbell

Mentor
This thread has been moved to its proper location. When posting a new question in the homework forums in the future, please follow the template that you will be given automatically, which organizes your information so we can follow it easily. It's obviously missing from this question because you didn't originally post in the homework forums.

#### gidoru90

Does nobody has an idea?! This will be a task in my exam on wednesday!

#### gidoru90

Is this topic really so difficult that nobody has even an idea?!
Just don't know how friction and the spring has to be connected...

#### Nathanael

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

F(Friction)=μk*F(Normal)
It isn't the kinetic friction you need to consider, it's the static friction.

What is in this case the normal Force (F(Normal))?
It is the component of m1*g that is perpendicular to the slope. Do you know how to calculate this?

F(Spring) + F(Friction) > F(Object2) + F(Object1) --> moves upwards
F(Spring) + F(Friction) < F(Object2) + F(Object1) --> moves downwards
You are close.

If the absolute value of F(Object2) + F(Object1) - F(Spring) > F(Friction) then m2 (and the whole system) moves.
If, on the other hand, $|F_{obj1}+F_{obj2}-F_{spring}|<F_{static.friction}$ then the system doesn't move.

Whether or not it moves depends on the absolute value of the forces.

Which way it moves is determined by whether the net force (you don't have to include friction) is positive or negative.

So when figuring out which way it moves, you don't need involve the force of friction (AS LONG AS you've already determined that it DOES in fact move).

(This is why I asked you to find out what had to be true for the system to move.)

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