How to Solve for Acceleration on Two Connected Incline Planes?

[Machinehead73]

Homework Statement

There are two ramps back to back one with a 4 degree incline and the other with a 15 degree incline the mass on the 4 degree is 4 lbs and the other is 24 lbs the 4 lbs mass has a coeffient of .2 and the 24 lbs mass has a coeffient of .4 the two masses have a rope connecting them. It wants me to solve for the accelleration and what direction this will go. I know how to solve if the masses were indepentent of each other, but how do you solve with the masses connent to one another?

Homework Equations

The Attempt at a Solution

 

[RoyalCat]

What I would do in this problem is make it a bit more simple, I'd "flatten" it out.

|m1|-------|m2|

I'd see what the component of gravity is pulling [tex]m_1[/tex] down, and what the component of gravity pulling [tex]m_2[/tex] down is. I would see which one is bigger, and that tells me which way the system accelerates. From there, I know which way the frictional forces point, and it becomes a simple matter of applying Newton's second law.

It's a bit hard to understand what I'm getting at from that diagram, if you've tried it and still don't understand, say so and I'll try and draw it out for you.

Irrelevant but useful if you're new to Physics:

Spoiler

You treat them as though they were independent, so to speak.

What you should do when you have a question about multiple masses is to draw what are known as "Free-body diagrams" for each of the masses. What I take note to do, is to always say what mass I'm referring to, what frame of reference I'm in (This isn't so important for you right now, since you're just getting started and only dealing with one frame of reference, the inertial one) and what the variable I'm looking to isolate from the equations is.

Draw all the forces acting on the mass, break them down according to a certain system of axes, and write the equations according to Newton's second law (For instance, if the mass does not rise up from the inclined plane, you can claim that the sum of forces along the direction perpendicular to the plane is 0), and since its accelerating in a certain direction, the sum of the forces along that axis is equal to [tex]m\vec a[/tex]

 

[Machinehead73]

I still do not understand

 

[RoyalCat]

I still do not understand

Okay, from the top. :)
Do you know what the components of the gravitational force, parallel to the incline and perpendicular to the incline are for each of the masses?

It'll be easier if we start working under the assumption that there is no friction, to see which way the system will 'tilt.' Will [tex]m_1[/tex] be pulling it down, or [tex]m_2[/tex]

Find out what force is pulling in the direction of the incline [tex]m_1[/tex] is on, and what force is pulling in the direction [tex]m_2[/tex] is on. See which one is bigger, that will tell you in which direction the system is accelerating.

Tell me once you've figured that out, or if there's something you haven't understood. And please be a bit more specific. ^^;

 

[Machinehead73]

Ok I did a free body dieagram for both the masses. I found Fn, Ff, Fp anf the Net force of the system. I was told I was wrong. I that I go the direction wrong. I figured if the weight of the 24lbs mass on the 14 degree incline would put the mass of the 4 lbs mass. But I was told this is not the case.

 

[RoyalCat]

Ok I did a free body dieagram for both the masses. I found Fn, Ff, Fp anf the Net force of the system. I was told I was wrong. I that I go the direction wrong. I figured if the weight of the 24lbs mass on the 14 degree incline would put the mass of the 4 lbs mass. But I was told this is not the case.

That's odd. Who told you that and did they explain why?

I see no reason why the 24 lb mass doesn't pull the 4 lb mass.

The forces of gravity in this tug o' war are [tex]24\sin{15^o} lb[/tex], [tex]4\sin{4^o} lb[/tex]
The 24 lb weight wins hands down. Bleh, given the coefficients, the system is decelerating, are you sure you wrote it down correctly?

 

[prob_solv]

the two masses have a rope connecting them.

What does this mean ?
Have you counted the tension of the string ( rope ) ?

 

[Machinehead73]

Did you figure the coeffient of friction in. And What is the acceleration? I am confused on this on It does not ask for tension in the rope.

 

[hotvette]

It might help to view this as two separate problems. One problem is a block sliding down an incline resisted by friction and an external force T1 (the rope). The 2nd problem is another block being pulled up an incline by an external force T2 (the rope) and resisted by friction. What can you say about T1 & T2?

What should have been included is the standard verbage something like "the blocks are connected by a massless rope (that can't stretch) over a frictionless pulley..."