Kinetic Energy / Potential Energy / Total Energy question

[Muu9]

Homework Statement

Object A is stationary while objects B and C are in motion. Forces from object A do 10 J of work on object B and -5 J of work on object C. Forces from the environment do 4J of work on object B and 8 J of work on object C. Objects B and C do not interact. What are delta K_tot and delta U_int if one system is defined to include objects A, B, and C and their interactions?

Relevant Equations

delta E = external work = delta K_tot + delta_U

W_ext is the external work done on B and C, which is 12 J
Delta K_tot is the internal work, which is the work done by A on B plus the work done by A on C
Delta K_tot = 5
Solving for \Delta U, we find that the change in potential energy is 7 J

This answer says otherwise: https://www.studysmarter.us/textboo...tionary-while-objects-are-in-motion-forces-f/

If Delta K_tot is not W_int, and instead delta U_int is -W_int, then W_int = 5 would imply delta U_int = -5

 

[PeroK]

Homework Statement:: Object A is stationary while objects B and C are in motion. Forces from object A do 10 J of work on object B and -5 J of work on object C. Forces from the environment do 4J of work on object B and 8 J of work on object C. Objects B and C do not interact. What are delta K_tot and delta U_tot if one system is defined to include objects A, B, and C and their interactions?
Relevant Equations:: delta E = external work = delta K_tot + delta_U

W_ext is the external work done on B and C, which is 12 J
Delta K_tot is the internal work, which is the work done by A on B plus the work done by A on C
Delta K_tot = 5
Solving for \Delta U, we find that the change in potential energy is 7 J

This answer says otherwise: https://www.studysmarter.us/textboo...tionary-while-objects-are-in-motion-forces-f/

I must admit I don't think I've seen a question like this before. I'm not entirely sure what they mean by internal energy, as opposed to kinetic energy.

 

[Muu9]

I must admit I don't think I've seen a question like this before. I'm not entirely sure what they mean by internal energy, as opposed to kinetic energy.

I think by Internal Energy they mean potential energy / U

 

[PeroK]

I think by Internal Energy they mean potential energy / U

I don't see that. There's nothing that implies potential energy.

 

[Muu9]

What is delta U_int?

 

[PeroK]

What is delta U_int?

I don't know. It may be physics, but not as I know it!

 

[Muu9]

This is the question itself:

 

[erobz]

This is the question itself:View attachment 322518

I can imagine $A$ having two springs. Say both $B$ and $C$ are moving to the right. One spring could be pushing $B$ to the right, and the other spring pushing $C$ to the left? They probably don't have to be springs. I'd imagine any mechanism that is releasing energy from $A$ could be doing this, and it could still be considered internal energy.

Then for the next part, the "environment" is somehow pushing both $B$ and $C$ to the right as well?

 

[PeroK]

What is delta U_int?

Here's a scenario that fits the problem statement.

$A$ is a person who is anchored to the ground. I.e. he/she cannot move.

$B$ is a box on wheels that is moving away from $A$. $A$ gives it a push with a pole, adding $10J$ of KE to $B$.

$C$ is another box on wheels moving towards $A$. $A$ gives it a push with his/her pole reducing its KE by $5J$.

Meanwhile, there is a strong wind blowing. The wind adds $4J$ of KE to $B$ and $8J$ of KE to $C$.

We know the change in KE of $B$ and $C$, but I don't see how to define "internal energy" in such a way that the changes caused by the wind differ fundamentally from the changes caused by $A$'s pole.

If, instead, $A, B$ and $C$ were in a box and the box was moving, then we would have the internal KE of the objects moving about inside the box (in the box's rest frame); and the motion of the (centre of mass) of the box itself. That would make sense.

Perhaps someone else will be able to interpret the question better than I can. Or, it's possible that this question is really not well posed.

 

[erobz]

Here's a scenario that fits the problem statement.

$A$ is a person who is anchored to the ground. I.e. he/she cannot move.

$B$ is a box on wheels that is moving away from $A$. $A$ gives it a push with a pole, adding $10J$ of KE to $B$.

$C$ is another box on wheels moving towards $A$. $A$ gives it a push with his/her pole reducing its KE by $5J$.

Meanwhile, there is a strong wind blowing. The wind adds $4J$ of KE to $B$ and $8J$ of KE to $C$.

We know the change in KE of $B$ and $C$, but I don't see how to define "internal energy" in such a way that the changes caused by the wind differ fundamentally from the changes caused by $A$'s pole.

If, instead, $A, B$ and $C$ were in a box and the box was moving, then we would have the internal KE of the objects moving about inside the box (in the box's rest frame); and the motion of the (centre of mass) of the box itself. That would make sense.

Perhaps someone else will be able to interpret the question better than I can. Or, it's possible that this question is really not well posed.

Thats how in interpret it.

However, if all of them were in a box, moving, $A$ is not stationary.

 

[PeroK]

Thats how in interpret it.

However, if all of them were in a box, moving, $A$ is not stationary.

Precisely! By Newton's third law, there must be an unspecified external force on A. Otherwise, B and C would exert equal and opposite forces on A.

 

[PeroK]

Thats how in interpret it.

However, if all of them were in a box, moving, $A$ is not stationary.

I supect the problem was written by someone with a vague knowledge of physics who just threw some things together with little understanding of what they were doing.

The whole problem and solution page isn't convincing to me.

 

[Muu9]

By the way, this is from Physics for Scientists and Engineers by Randall Knight

 

[PeroK]

By the way, this is from Physics for Scientists and Engineers by Randall Knight

Gets good reviews, so what do I know?

 

[haruspex]

The question seems to expect expressions for ΔK and ΔU for B and C separately. I don't see how that is possible. We would need to be able to distinguish the work done on an object by the net force (ΔK) from the net work done by the forces (ΔK+ΔU).
Even in (b), having multiple forces from the environment creates the same problem; we cannot tell what happens to the KE of the mass centre.