A physics problem involving an inclined plane and a block

[carrotstien]

This is a problem that i thought up, not a homework problem!

There is an incline plane of Mass Ma, whose incline is at an angle theta with the horizontal. There is a block on this incline whose mass is Mb. There is no friction or gravity. There is a horizontal leftwards force applied on the inclined planeto push it to the left. The push would cause the small block to rise and accelerate. The inclined plane is either attached to a horizontal rail, or is a double sided incline plane and rests on a frictionless surface so to ignore the torque created by the inertia of the block around the right angle vertex of the incline. The force pushing the plane to the left is Fext. What is the acceleration of the block relative to an inertial reference frame.

I tried to solve it, and when i thought i finally got the right answer it came out to be logically incorrect when i graphed it.

Can anyone solve it and show the work?

If you can't then check out the attachment. Thats what I tried. I don't see anything wrong with any of my logical steps, but the final result only looks normal on the graph when the mass of the small block is less than that of the inclined plane. But the ratio shouldn't affect the resulting graph shape.

 

[robb_]

I only looked at you FBD for both masses. There are forces missing (these blocks are on a planet right?) and the force by the rail is incorrectly shown.

 

[carrotstien]

no planet, no gravity. The purpose of the rail is to just prevent any motion other than parralel to it. I'm not counting torques or anything. If it wasn't for a rail, if the incline was just resting on a surface, then pushing the incline in the direction shown would cause it to rotate. The forces shown for the rails, may be in wrong directions, but they are vectors, and a negative vector in one direction is just a positive in the opposite direction.

 

[robb_]

Your problem seems complicated.
To me it looks as if the wedge has a net force "down" on it.

 

[carrotstien]

huh

what do u mean it looks like it has a net force down? Do you mean that the force diagram makes it seem like it has a net force down? The direction of the vectors for the rail gripings (wtver) is not specific, they could be in the opposite direction, the only thing the rail does is cancel out any vertical force upon the inclined plane.

 

[robb_]

Yes, I meant that your force diagram implies that.

 

[carrotstien]

that still doesn't change the fact that i can't get the answer, and i can't find anyone that could. I already, 2 different ways, came to the same wrong conclusion. This "wrongness" amplifies dramatically when i input the mass of A to be much smaller than B. Infact, when I input the mass of A to be .001, the acceleration of B ends up to be 70 m/s^2 when theta is .8103 degrees and when the force is 10, and the mass of B is 5.

This can't be correct, or atleast it shouldn't be correct by common sense. How could a force of 10 Newtons, push on a system with a mass of 5.001 kg and result in the block accelerated at 70m/s^2. If this is how it would work in real life, than I'm correct in my conclusion...but i doubt it.

 

[denverdoc]

I looked at the problem, and am wondering in what inertial frame you get the results mentioned. Let's say that the incline is the observer.

lets further suppose that the incline is zero degrees.

the acceleration to a stationary observer for block b would be zero, with mass of .001, 5 and f=10N.

But in the other instance relative to the "incline" it would be 10,000m/s^2.

 

[carrotstien]

i'm counting everything in the inertial reference frame, if i wasn't, then at 90 degrees, the v and a of block B woudl be 0 (with respect to the incline)

 

[denverdoc]

agree with that statement re a perpendicular incline. maybe i'll sit down and give this a try.

 

[denverdoc]

now that I give it a seconds thought, your result may indeed make sense in this situation; say in space, far beyond any planets, where the only gravitational force is between the two masses themselves. Since there is no gravity, no friction, and no normal force per se, if one were to kick the incline hard, it would seem that the block would rise rapidly. Up at least until the time the incline slid out from underneath the block. This is just a mathless seat of the pants intuitive approach, based on the results you implied--if perpendicular, Vy=0 and a(x)=fe/(Ma+Mb) and the other extreme, also Vy=0,
Mb remains stationary while Mb flies off under tremendous acceleration. I think i agree that the only mass that is inertial is all of that of the incline and sin(theta)*Mb

 

[carrotstien]

But that would mean that it is possible to push something faster indirectly than directly! So if the angle is 1 degree, then a push of 10 Newtons, would result in a force much greater than 10 Newtons almost vertically upwards upon the block (in the case where the incline is massless, or nearly massless)

 

[carrotstien]

hmm, now its kind of making sense. I thought about this case:

You have a building, or super heavy block. You place two wedge at teh base on both sides of the block. Then you push with some small force. If there is no friction between the wedge and the block, then the only force resisting your push on each side is sin(theta) mg. If you make theta very very small, this force could become smaller than ur force. This will result in you picking up the block. In order to lift up the block, you would need to apply a force of atleast mg vertically. That would mean, that while you may be applying as little as 10 Newtons sideways, your wedge would appy 1000's of Newtons vertically upon the building/block. This doesn't work in real life due to friction, but where there is no friction it works.

So i guess i did solve the problem.