FRICTIONLESS INCLINED PLANE.. (some guidance please)

[arildno]

Oops; I didn't see the condition in the original problem that m should not slide relative to M..

 

[plusaf]

thank you!

Oops; I didn't see the condition in the original problem that m should not slide relative to M..

yes, it looked to me that, in the notes flying back and forth, that point was missed, and it's one key to a correct solution.

look at limit cases: if they're all frictionless surfaces, a low force (or acceleration) will let the small mass slide down the ramp. (best example: no acceleration of the large mass, at all!)
a very high acceleration (force) applied to the large mass will accelerate it very quickly, and the small mass will zip UP the ramp (and presumably, be left behind... )

next "easy-see" boundary conditions: if the ramp has zero slope, any acceleration at all to it will enable the small mass to go "up" the ramp. if the ramp has an angle of 90 degrees, it there is no acceleration that can possibly keep the smaller block from going "down the ramp".

the correct answer lies inbetween these corner cases.

calculate on, folks! i expect a correct answer to appear here, now, in a matter of days, if not minutes!

good thinking (and a good re-read of the original question, too!

 

[plusaf]

correct!

If I'm picturing the problem correctly, both blocks will have a horizontal acceleration to the right. (For the condition that m not to slide down M.) This is the direction that A shows in the drawing.

that's my take on it!

note, please, the phrase in the original question, which i think misled the original poster as well as many others: "(how?) Fast must the inclined plane be moving in order for the mass to stay exactly where it is."

at any constant speed, the mass must and will slide down the ramp! the only way to prevent that is to "accelerate it up the plane just as fast as it would have been accelerating down the plane" if the bigger block weren't moving! the two accelerations must cancel for the small block to not move.

 

[Doc Al]

calculate on, folks! i expect a correct answer to appear here, now, in a matter of days, if not minutes!

The problem remains as simple to solve as ever. As I pointed out in post #3 of this thread, the key is finding the acceleration of the sliding mass given the constraints of the forces on it. Once that's found, then you can find the force that needs to be applied to the incline to produce that acceleration. (I assume that the real problem is to find the applied force; certainly not the speed, as the original poster mistakenly wrote.)

Still waiting for the original poster to solve it for himself.