# Kinetic Energy / Potential Energy / Total Energy question

• Muu9
In summary, the problem statement involves an object A that is stationary while objects B and C are in motion. A does 10 J of work on B and -5 J of work on C, while the environment does 4 J of work on B and 8 J of work on C. The question asks for the change in total kinetic energy (delta K_tot) and total internal energy (delta U_tot) of the system consisting of objects A, B, and C and their interactions. However, it is unclear how to define internal energy in this scenario.

#### 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

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

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Muu9 said:
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

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.

MatinSAR
PeroK said:
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

Muu9 said:
I think by Internal Energy they mean potential energy / U
I don't see that. There's nothing that implies potential energy.

What is delta U_int?

Muu9 said:
What is delta U_int?
I don't know. It may be physics, but not as I know it!

This is the question itself:

Muu9 said:
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?

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Muu9 said:
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.

PeroK said:
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.

erobz said:
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.

erobz said:
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.

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

Muu9 said:
By the way, this is from Physics for Scientists and Engineers by Randall Knight
Gets good reviews, so what do I know?

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.