Two masses connect by a rope over unequal slopes

[savva]

Hey Guys,

I'm stuck with two particular problems that relates to two masses attached by a rope on a slope with unequal angles and I'm unsure how to go about the problem, I have never accounted a problem such as these before and I'm stuck with how to go about it. I have taken two photos of the questions as they include a diagram!

Thanks in advanced.

Homework Statement

Q.9 and Q.19 are those I am referring to in the attachments.

Homework Equations

I believe looking at all the forces affecting the diagram, Tension, Gravity, Weight components, ultimately to my understanding ƩF=0 for the block to remain at rest, that is the forces balance. I am a bit confused on how to set out some of the forces as most problems I have encounted similar to this have a 90 degree angle where the block on the left is.

The Attempt at a Solution

I do not have answers to these two questions as they are not provided with the textbook

 

[estro]

For each mass try writing sum of all forces in x and y direction. [and show us how you wrote them]

Without going into calculations my intuition tells me the system will move to the left. [if there is no friction, can you tell what is the friction needed to keep the system at rest?]

 

[savva]

For each mass try writing sum of all forces in x and y direction. [and show us how you wrote them]

Without going into calculations my intuition tells me the system will move to the left. [if there is no friction, can you tell what is the friction needed to keep the system at rest?]

I don't know, I'm confused, I know the only possible forces that can act is tension and weight components but I don't know how to set it out. Here is an attempt anyway

F1=F2

F1:
x: mgcosθ
y: T-mgsinθ

F2:
x: T-mgcosθ
y: T-mgsinθ

 

[estro]

1. Draw the system with all the forces, you don't need x and y as for both the masses all the relevant forces are in 1 dimension, choose the direction parallel to the slope. [in the other dimension sum of all forces are 0...]
2. Don't forget the Newton laws.
3. You will have 2 equations with two unknowns, do you know what they are?

Let your intuition help you.
Hint: What can you tell about a? [$\sum F=ma$]

 

[estro]

Another hint, for each mass draw its own diagram and choose the coordinate system parallel to the slope.