Work done by action reaction forces when they move things

[Let'sthink]

TL;DR Summary

A point mass m slides down the smooth surface (of length L) inclined at an angle θ) of wedge of mass M kept on a smooth horizontal plane. The height of the wedge is H and base B. Discuss their motion and find time when they separate and their velocities when they separate.
This is not homework.

Normally action reaction forces do not move things. In this problem they move. I wish to discuss in what way these so called constrain forces contributeto motion or kinetic energy L. Do they do wirk. Yes then why no then why not?

 

[anuttarasammyak]

In a wider view of action-reaction, a mass is pulled by the Earth. The Earth is pulled by a mass with same amount of force.

 

[Let'sthink]

Please first state what kind of motion do you expect for block of mass m and Incline of Mass M. Will reaction force be mg cos theta or will it be different?

 

[anuttarasammyak]

Will reaction force be mg cos theta or will it be different?

The gravity force normal to the slope is mg cos theta. It cancells with force from slope.

 

[erobz]

Will reaction force be mg cos theta or will it be different?

By reaction force you mean normal force of contact between the point mass $m$ and the incline of mass$M$. Try writing Newtons 2^nd Law for each free body. Once you have them you can investigate whether or not what you are asking holds.

Please see LaTeX Guide for formatting mathematics

 

[anuttarasammyak]

Normally action reaction forces do not move things.

They can move because action force is applied to A from B and reaction force is to B from A. They are not cancelling forces applied to the same mass.

 

[A.T.]

Normally action reaction forces do not move things.

What do you mean here? All interaction forces obey Newton's 3rd Law (if that's what you mean by "action reaction forces"). The acceleration depends on the total force on each object (Newton's 2nd Law).

 

[Let'sthink]

What is fundamental difference between forces of interaction between objects even from a distance and so called action reaction forces of constraint between two bodies in contact or constrained to be in contact?

 

[Let'sthink]

B

What is the magnitude of reaction force still mg cos theta or different?

 

[Let'sthink]

By reaction force you mean normal force of contact between the point mass $m$ and the incline of mass$M$. Try writing Newtons 2^nd Law for each free body. Once you have them you can investigate whether or not what you are asking holds.

Please see LaTeX Guide for formatting mathematics

This is not my homework. I have already derived the expression. I am posting for the purpose of stimulating discussion to bring out fundamental difference difference between forces of constraint and forces of interaction which can be expression terms of distance between them.

 

[anuttarasammyak]

What is the magnitude of reaction force still mg cos theta or different?

Say A is the mass and B is the Earth including the slope.
Force from B to A is $m\mathbf{g} + \mathbf{N}$
Force from A to B is $-m\mathbf{g} - \mathbf{N}$
where N is force transmitted from B to A at slope plane. These coupled forces satisfing
$$F(B\rightarrow A) =- F(A \rightarrow B)$$ are called action and reaction.

The constraint that the mass stays on the slope is realized by the balance of N and mg $\cos \theta$, the normal-to-slope component of $m \mathbf{g}$. Mass does not move in noral direction of the slope if initially it is on the slope. Please be careful that N and mg $\cos \theta$ which are applying on the SAME body, are not action and reaction which are applying to DIFFERENT bodies in interaction, e.g., A and B in the above example.

BTW Why don‘t you apply y=$\tan \theta$ x, where x and y are the coordinates of the mass, for the constraint condition of your problem ?

 

[A.T.]

What is fundamental difference between forces of interaction between objects even from a distance and so called action reaction forces of constraint between two bodies in contact or constrained to be in contact?

Newton's 3rd Law (usually associated with "action and reaction") applies to all interaction forces (contact and distant).

Constraint forces are a subset of interaction forces. They usually act to constrain the relative kinematics between two bodies. They do this by automatically adjusting themselves, based on other forces acting simultaneously on those bodies, to make the net force consistent with certain kinematics (Newton's 2nd Law). Some people might call that also "action and reaction", but it is a completely different meaning than above.

In either case, the action-reaction-terminology adds nothing to the actual physics, so I would advice to avoid it completely.

 

[sophiecentaur]

TL;DR Summary: A point mass m slides down the smooth surface (of length L) inclined at an angle θ) of wedge of mass M kept on a smooth horizontal plane. The height of the wedge is H and base B. Discuss their motion and find time when they separate and their velocities when they separate.
This is not homework.

In this problem they move.

I have a feeling that you have the old 'classification problem'. I think you are conflating action and reaction with equilibrium and see a contradiction. N3 always applies; N2 deals with different pairs of forces.

Third Law pairs are involved in motion and each 'does work' in many situations. The only time they don't is when the net value of all the forces is zero. But the magnitude of an action force is always the same as the magnitude of the reaction force; that net force is zero. In your Summary you must use all the correct forces to decide whether or not work has been done.
Edit.... And, to state the obvious, the work done 'by' one of those forces is equal and opposite sign to the work done 'by' the other one. In cases where there is internal movement (e.g. stretch on a string or squashing of a coupling) the actual motion may be different and that will involve loss of energy

 

[erobz]

This is not my homework. I have already derived the expression.

Just clarify, and discussion can begin? I'm pretty sure most of us like to go into the equations to get/examine necessary insights (at least I do).

What is the magnitude of reaction force still mg cos theta or different?

If you are not sure about this, then you seemingly have the expression wrong. Why don't you just post the expression and derivation for $N$ (the normal contact force from the (accelerating) slope acting on the point mass)? My opinion is that it is definitely not that expression in general for this problem.