Object A is stationary while objects B and C are in motion.

[Cc518]

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 4 J of work
on object B and 8 J of work on object C. Objects B and C do
not interact. What are ΔKtot and ΔU if (a) objects A, B, and C
are defined as separate systems and (b) one system is defined to
include
objects A, B, and C and their interactions?

Homework Equations

ΔEsys 2 = ΔKtot + ΔU = (WA + WB+WC) + ΔU = 0

The Attempt at a Solution

I get WB=14J and WC=3J. I just don't understand why WA is not -5J. Apparently C and B exert forces onto A, right? So ΔKtot = 14 + 13 -5 =12J, but the answer is 17J.
For part B, I thought ΔU = -ΔKtot= -12J, but the answer is -5J.

Any help is appreciated!

 

[haruspex]

why WA is not -5J

By some unspecified means, A remains stationary. How is the work done on an object defined?

 

[Cc518]

By some unspecified means, A remains stationary. How is the work done on an object defined?

No work acting on A because no net force exerted on A?

 

[haruspex]

No work acting on A because no net force exerted on A?

That's not what I asked. How is the work done on a body defined?

 

[Cc518]

That's not what I asked. How is the work done on a body defined?

The body has to move a distance d

 

[haruspex]

The body has to move a distance d

Ok, maybe it is not the definition as such, but this is what I mean:

https://en.wikipedia.org/wiki/Work_(physics)#Work–energy_principle
"the work done by all forces acting on a particle (the work of the resultant force) equals the change in the kinetic energy of the particle".

So how much work is done on A?

 

[Cc518]

A is stationary which means its velocity doesn't change, therefore its change in kinetic energy is zero, therefore the work done on A is zero

 

[haruspex]

A is stationary which means its velocity doesn't change, therefore its change in kinetic energy is zero, therefore the work done on A is zero

Right.
Does that also answer your query on part b?

 

[Cc518]

So if we consider A, B and C as one system, the ΔKtot is 14 + 13 =17J. Then the change in potential energy should be -17J since the energy is conserved in an isolated system, am I correct?
But the answer says change in potential energy is 5J, I don't understand

 

[haruspex]

the energy is conserved in an isolated system

But it is not isolated. If it were, A would move, and we are anyway told that external forces do work on B and C.

 

[Cc518]

Sorry, I still don't understand how WA=0(work done on A equals zero) helps me to understand part b...
If we only consider the interactions between A,B and C, excluding the external forces, the total change in kinetic energy is WB+WC=10-5=5J, which makes the total change in potential energy equal to - ΔKtot=-5J in a system consisting A, B and C. Am I right?

 

[haruspex]

If we only consider the interactions between A,B and C, excluding the external forces, the total change in kinetic energy is WB+WC=10-5=5J, which makes the total change in potential energy equal to - ΔKtot=-5J in a system consisting A, B and C. Am I right?

Yes, I think so.

 

[Cc518]

OK，thank you so much!