Block moving on a horizontal surface

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Vibhor
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Homework Statement



Diagram of a cube with a smooth inclined groove on its vertical face at 30 degrees to the horizontal, with a cylinder A in the groove and an arrow a0 pointing left along the base.


Homework Equations

The Attempt at a Solution



Working from the reference frame of block , a pseudo force Ma0 towards right need to be applied on the cylinder .

Forces acting on the cylinder are pseudo force , weight Mg and normal force from the block (if any) .

Since the cylinder does not have horizontal acceleration , N sin30° = Ma0 .

I am not able to proceed from here .

Any help would be appreciated .
 
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  • Diagram of a cube with a smooth inclined groove at 30 degrees to the horizontal in its vertical face, with cylinder A sitting in the groove and an arrow labelled a0 pointing left from the cube's left side.
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Vibhor said:

Homework Statement



Diagram of a cube with a smooth inclined groove at 30 degrees to the horizontal in its vertical face, containing cylinder A; the cube accelerates horizontally to the left with acceleration a0 along the bottom surface.


Homework Equations

The Attempt at a Solution



Working from the reference frame of block , a pseudo force Ma0 towards right need to be applied on the cylinder .

Forces acting on the cylinder are pseudo force , weight Mg and normal force from the block (if any) .

Since the cylinder does not have horizontal acceleration , N sin30° = Ma0 .

I am not able to proceed from here .

Any help would be appreciated .

The cylinder does not have horizontal acceleration in the rest frame of reference. So it accelerates with respect to the slope.
 
ehild said:
The cylinder does not have horizontal acceleration in the rest frame of reference. So it accelerates with respect to the slope.

Sorry , i did not understand . Could you please explain it a bit more . Do you think the application of pseudo force and subsequent equation written in the block frame are wrong ?
 
You assumed that the horizontal acceleration of the cylinder is zero in the block frame of reference, didn't you?
 
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ehild said:
You assumed that the horizontal acceleration of the cylinder is zero in the block frame of reference, didn't you?

Yes .

So , should the equation be Ma0 - N sin30° = Ma ( 'a' is the horizontal acceleration of the cylinder in the block frame ) ?
 
If the cylinder does not accelerate horizontally with respect to the block, what is its (horizontal) acceleration with respect to the ground?
 
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ehild said:
If the cylinder does not accelerate horizontally with respect to the block, what is its (horizontal) acceleration with respect to the ground?

I guess you wanted to ask the other way round :smile: .

Anyways , (horizontal) acceleration with respect to the block would be a0 . That would give N = 0 .

Now ,how should I calculate value of a0 ?
 
What is the vertical acceleration? There is some geometric relation between the horizontal and vertical acceleration of the block in the grove.