Inclined plane force components and the acceleration problem

[goktr001]

Homework Statement

There is no variable for it but we know the angel σ, g, the mass of m₁ and m₂, m₂>m₁ and the coordinate system must be considered like that. I know the other method which the coordinate system is parallel to the inclined plane's hypotenuse.

Homework Equations

F=m*a
Newton's Second Law: ƩF=m.a

The Attempt at a Solution

Here is a diagram of the what I'm talking about. I found the forces and some equations but I cannot find the acceleration of the system from the datas I found. And I'm not sure if the Normal Force(N) must be considered? Thanks for all the helps.

 

[PhanthomJay]

This choice of coordinate system is more difficult to work with, because the block on the plane accelerates along both axes. As in any free body diagram, all forces must be identified, including the normal force. Then apply Newton's laws in the x and y directions for each mass. Be sure to correctly identify the components of the normal force.

 

[goktr001]

This choice of coordinate system is more difficult to work with, because the block on the plane accelerates along both axes. As in any free body diagram, all forces must be identified, including the normal force. Then apply Newton's laws in the x and y directions for each mass. Be sure to correctly identify the components of the normal force.

I know my way is the diffucult way but our college professor wants the solution in this way. OK, I will add the normal force too; but now, must the acceleration be divided for both x and y axes? So how can I solve this question? I find all the components but then I couldn't find out how I can calculate the accelaration. Thanks.

And for applying Newton's laws. Yes, it's so easy to find it for m1, but m2 is really hard one. I even cannot apply Newton's law on the second mass. The problem is that actually.

 

[PhanthomJay]

You have already designated the x and y components of the acceleration as a cos theta and a sin theta. You should now break up the normal force, which acts perpendicular to the incline, into its x and y components. And break up the tension force T into its x and y components . Now use Newton 2 on the first mass in the y direction, Newton 2 on the 2nd mass in the x direction, and Newton 2 on the 2nd mass in the y direction, and you get three equations with 3 unknowns, a, T, and N, solve for all.

 

[goktr001]

You have already designated the x and y components of the acceleration as a cos theta and a sin theta. You should now break up the normal force, which acts perpendicular to the incline, into its x and y components. And break up the tension force T into its x and y components . Now use Newton 2 on the first mass in the y direction, Newton 2 on the 2nd mass in the x direction, and Newton 2 on the 2nd mass in the y direction, and you get three equations with 3 unknowns, a, T, and N, solve for all.

Then, are all these true now? I'm really sorry for my poor English, and thanks for all your help.

• (1) Using of Newton 2 on the first mass in the y direction = T-m₁.g=m₁.a
• (2) Using of Newton 2 on the second mass in the y direction = m₂.g-T.sinσ-N.cosσ=m₂.a.sinσ
• (3) Using of Newton 2 on the second mass in the x direction = N.sinσ-T.cosσ=m₂.a.cosσ

For the acceleration, in which order I have to use these equations, if you may answer. I couldn't solve for N, T and a because of these sin and cos'. Anyway thanks for your help again :)

 

[goktr001]

I've just found the acceleration! Thanks for all the helps :) I found it by eliminating the normal force from the equations by dividing two equations to each other.

a = g.(m2.sinO-m1)/m1+m2