Block moving on a horizontal surface

In summary, the problem involves a cylinder on a slope, with the reference frame being the block. The cylinder does not have horizontal acceleration in this frame, so a pseudo force is applied towards the right. The forces acting on the cylinder are the pseudo force, weight, and normal force from the block. The equation N sin30° = Ma0 is used, but there is difficulty in proceeding further. The horizontal acceleration of the cylinder with respect to the ground is needed in order to solve the problem. There is a geometric relation between the horizontal and vertical acceleration of the block in the groove.
  • #1
Vibhor
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Homework Statement



?temp_hash=1b1eef46b89857e8bb7424f18d3afa48.gif


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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  • #2
Vibhor said:

Homework Statement



?temp_hash=1b1eef46b89857e8bb7424f18d3afa48.gif


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.
 
  • #3
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 ?
 
  • #4
You assumed that the horizontal acceleration of the cylinder is zero in the block frame of reference, didn't you?
 
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  • #5
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 ) ?
 
  • #6
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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  • #7
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 ?
 
  • #8
What is the vertical acceleration? There is some geometric relation between the horizontal and vertical acceleration of the block in the grove.
 
  • #9
Thank you very much :smile: .
 

Related to Block moving on a horizontal surface

1. How does friction affect the movement of a block on a horizontal surface?

Friction is a force that opposes the movement of objects in contact with each other. In the case of a block on a horizontal surface, friction acts in the opposite direction of the block's motion, slowing it down or preventing it from moving altogether.

2. What factors influence the amount of friction between a block and a horizontal surface?

The amount of friction between a block and a horizontal surface depends on the type of surface, the weight of the block, and the force applied to the block. Rough surfaces and heavier blocks typically have more friction, while smoother surfaces and lighter blocks have less friction.

3. How does the angle of the surface affect the movement of the block?

The angle of the surface can affect the movement of the block in two ways. If the surface is inclined, the block will experience a downward force due to gravity, making it harder to move. If the surface is tilted, the block may slide or roll in a specific direction depending on the force applied.

4. What is the difference between static and kinetic friction?

Static friction is the force that must be overcome to set an object in motion, while kinetic friction is the force that opposes the motion of an object. In the case of a block on a horizontal surface, static friction keeps the block from moving until a force is applied, while kinetic friction acts to slow down the block's movement.

5. How can the coefficient of friction be calculated for a block on a horizontal surface?

The coefficient of friction can be calculated by dividing the force of friction by the normal force between the block and the surface. The normal force is equal to the weight of the block, and the force of friction can be measured by the force needed to move the block or by the acceleration of the block.

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