FRICTIONLESS INCLINED PLANE.. (some guidance please)

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Homework Help Overview

The problem involves an inclined plane with a mass on it, both of which are frictionless. The goal is to determine the necessary speed of the inclined plane to keep the mass stationary relative to it. The scenario includes gravitational effects and requires consideration of forces acting on the mass.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for the inclined plane to accelerate to prevent the mass from sliding down. They explore the forces acting on the mass, including gravitational force and normal force, and consider how to set up equations using Newton's laws. Some participants express uncertainty about the components of forces and the necessary calculations.

Discussion Status

There is ongoing exploration of the problem, with participants attempting to clarify their understanding of the forces involved. Some have provided hints and suggestions for drawing diagrams and setting up equations, while others are still working through their reasoning and calculations without reaching a consensus.

Contextual Notes

Participants note the frictionless nature of the surfaces and the specific gravitational acceleration value provided. There is also mention of the need to consider both the inclined plane and the mass together when calculating the required force for acceleration.

  • #31
Oops; I didn't see the condition in the original problem that m should not slide relative to M..:redface:
 
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  • #32
thank you!

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

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... :smile: )

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!

:approve:
 
  • #33
correct!

Doc Al said:
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.


:approve:
 
Last edited:
  • #34
plusaf said:
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. :smile:
 

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