Virtual displacement for a block sliding down a wedge

• Kashmir
In summary, the virtual displacements for the two block system are different depending on whether the small block is constrained to move vertically downwards or horizontally.
Kashmir

A block slides on a frictionless wedge which rests on a smooth horizontal plane. There are two constraints in this system. One that the wedge can only move horizontally and another that the block must remain in contact with the wedge.

We want to find the virtual displacements for the two block system.

To find those virtual displacements we imagine to freeze the constraints and look for the possible displacements.

Now if I freeze the constraints then the wedge cannot move. The only possible motion is that the small block slides parallal along the incline. However I have found on many articles online that there is a virtual displacement for the wedge as well.

This confuses me how to view the virtual displacements in this case. Can anyone please explain this. Thank you.

Imagine what happens if the small block is constrained to move vertically downwards. The wedge would be squeezed and pushed to the left. Similar to squeezing a slippery melon seed between fingers.

CWatters said:
Imagine what happens if the small block is constrained to move vertically downwards. The wedge would be squeezed and pushed to the left. Similar to squeezing a slippery melon seed between fingers.
I don't think that helps with the question being asked, namely, how one is supposed to apply the method of virtual displacement here.
It's not a method I am au fait with, so I won't attempt to write an answer.
@Kashmir , see if page 31 onwards of https://www.worldscientific.com/doi/pdf/10.1142/9789810248154_0002 helps.

1. What is virtual displacement for a block sliding down a wedge?

Virtual displacement is a concept used in physics to analyze the motion of objects without actually physically displacing them. In the case of a block sliding down a wedge, it refers to the hypothetical displacement of the block along the wedge's surface without any external forces acting on it.

2. How is virtual displacement calculated for a block sliding down a wedge?

Virtual displacement is calculated by determining the change in position of the block along the wedge's surface in small increments. This is done by considering the geometry of the wedge and the angle at which the block slides down, as well as the forces acting on the block.

3. What is the significance of virtual displacement in the analysis of a block sliding down a wedge?

Virtual displacement allows us to mathematically analyze the motion of the block without taking into account the effects of friction or other external forces. This helps simplify the problem and allows us to focus on the fundamental principles of motion and energy.

4. How does virtual displacement relate to the concept of work in physics?

In physics, work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. Virtual displacement allows us to calculate the work done on the block as it slides down the wedge, without actually moving the block.

5. Can virtual displacement be used to calculate the acceleration of the block sliding down a wedge?

Yes, virtual displacement can be used to calculate the acceleration of the block. By considering the forces acting on the block and its virtual displacement, we can use Newton's second law of motion (F=ma) to determine the acceleration of the block as it slides down the wedge.

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