What happens when an inclined plane can move freely?

[konichiwa2x]

Hi,
I recently did a problem in which a block of definite mass was placed on the top of a inclined plane which was inclined at some angle with the horizontal. The block starts to slide down. What would happen if the inclined plane was not fixed?

 

[Hootenanny]

Hi,
I recently did a problem in which a block of definite mass was placed on the top of a inclined plane which was inclined at some angle with the horizontal. The block starts to slide down. What would happen if the inclined plane was not fixed?

What do yo think would happen?

 

[konichiwa2x]

well I think there won't be any effect i.e, it would be the same as if it was fixed. is that right?

 

[Doc Al]

No. Answer this question: Does the inclined plane exert a force on the block?

Then consider Newton's 3rd law.

 

[rcgldr]

The movement(s) will depend on the mass of the block and plane, and the coefficient of friction between block/plane and plane/floor.

Imagine what would happen if you had a 50 lb block of ice on a 10 lb 45 degree metal plane on a sheet of ice.

 

[konichiwa2x]

No. Answer this question: Does the inclined plane exert a force on the block?

Then consider Newton's 3rd law.

yes , mgcos$$\theta$$ if $$\theta$$ is the inclination of the inclined planed with respect to the horizontal. So that means the block also exerts a force equal in magnitude on the inc. plane. I think if the magnitude of this force is large enough, the inclined plane will move . But I am not sure in which direction. Is this correct?

 

[Hootenanny]

yes , mgcos$$\theta$$ if $$\theta$$ is the inclination of the inclined planed with respect to the horizontal. So that means the block also exerts a force equal in magnitude on the inc. plane. I think if the magnitude of this force is large enough, the inclined plane will move . But I am not sure in which direction. Is this correct?

Yes, this is correct. Try drawing a free body diagram and examine the forces. You may also wish to note that conservation of momentum applies here.

 

[Doc Al]

yes , mgcos$$\theta$$ if $$\theta$$ is the inclination of the inclined planed with respect to the horizontal.

Careful. The force that the incline plane exerts on the block--the normal force--will only equal $mg\cos\theta$ if the plane does not accelerate.

So that means the block also exerts a force equal in magnitude on the inc. plane.

Yes, that is exactly the point.

I think if the magnitude of this force is large enough, the inclined plane will move . But I am not sure in which direction. Is this correct?

Yes. A simple case to analyze is when the inclined plane slides without friction.

The direction that the inclined plane will move is easy to determine. The only horizontal force on the plane is the normal force exerted by the block on the plane. If you draw a diagram showing the forces acting (as Hoot suggests) you will quickly see which way that force acts.