Curious about Work and Energy Consumption

[John Constantine]

TL;DR Summary

Work and Energy Consumption

I asked a similar question yesterday, but I have additional queries, so I'm posting another question. If I pull an object connected to a string with a force of 10N in a straight line for 1 meter, I would have done 10J of work on the object. According to the law of conservation of energy, I would lose 10J of energy, and the object would gain 10J of energy (Of course, the human body's structure is more complex, so it might lose more energy, but I'll omit such details).

Now, imagine a spring placed between me, fixed to the ground, and the object, and the spring compresses or extends as it moves the object. The spring would compress, and the object would move.

In this situation, does the work I do on the object exist? (i.e., do I lose energy?) If I pull the spring with a force F1, and the object moves by a distance d in that direction, wouldn’t there be work done by the specific force F1? Common sense suggests that if an object is hanging from a spring attached to a fixed wall and the spring compresses, the work done by the wall on the object should be zero, but if there is work done by F1, what work cancels it out?

 

[John Constantine]

The energy (work) gained by the object results in a decrease in my energy. I understand that it's important to properly define the system to determine the work done on the object. If an object is hanging from a string and I pull the string, the work I do on the object might be considered zero if we define only the object as the system, yet my energy is clearly consumed. I understand this as 'to know the energy consumption of the object, you need to define the system that includes the interaction between the object and the subject.' If further explanation is needed, can you provide more details about this?

 

[russ_watters]

So:
1. Yes, these principles are true.
2. You have to properly define your system and not play bait-and-switch games with it. Keep track of the work/energy faithfully and you'll never have a problem.
3. The efficiency of the human body is exceptionally poor (even sometimes negative) and isn't great for this tracking.

 

[Dale]

I understand that it's important to properly define the system to determine the work done on the object.

Excellent, so let’s start there. What is your system? Your system should be chosen such that the force of interest is an external force acting on the system.

Once you have clearly identified that, the next step is to draw a free body diagram. Identify and label all of the external forces acting on the system.

Then you start writing equations, such as conservation laws or Newtons laws or Hooke’s law, etc.

If an object is hanging from a string and I pull the string, the work I do on the object might be considered zero if we define only the object as the system, yet my energy is clearly consumed. I understand this as 'to know the energy consumption of the object, you need to define the system that includes the interaction between the object and the subject.'

Yes, essentially. If the interest is determining the amount of work done by your pulling force then your pulling force needs to be an external force acting on the system. So defining the system as only the object would be a bad choice because it won’t help you analyze the quantity of interest.

Note, you would not consider the work to be zero. It would be undetermined. Undetermined quantities are not just arbitrarily set to zero.

 

[John Constantine]

If the force I applied to the object through the string made the object move, then considering the string and the object as one system, it means I did work on the object. In contrast, is it that the reaction force of "the force the spring applied to me," which is "the force I applied to the spring," does not get transmitted to the object, resulting in zero work done? I can still do work on the object even if I am not directly applying force to it. In a similar manner to yesterday's case, "the force I applied to the string" corresponds to "the force I applied to the spring," and the object certainly moves, so why is it that when connected to a spring, the work done is zero?

 

[A.T.]

I can still do work on the object even if I am not directly applying force to it.

If you model the spring as a separate object, then you are not doing work on the mass, just on the spring. And the spring is doing work on the mass.

If you model the mass & spring as one object, and then your force is applied directly to that object and you are doing work on it.

It's your choice to make. All your questions seem to stem from failure to decide how you want to model it.

 

[Dale]

considering the string and the object as one system, it means I did work on the object

No. It means you did work on the system, which is the string plus the object. If your analysis treats the string and object as the system then you cannot make separate conclusions about the object.

Note that it is possible to have multiple systems. So if your interest is both in the work done by you and the work done on the object then you would model the string as one system and the spring as another system.

You would then find that you do work on the string and the string does work on the object. You would not find that you do work on the object.

In contrast, is it that the reaction force of "the force the spring applied to me," which is "the force I applied to the spring," does not get transmitted to the object, resulting in zero work done?

What is your system (or systems) here? Remember, you should define your system (or systems) so that the quantities of interest are external forces acting on (one of) the system(s)

I can still do work on the object even if I am not directly applying force to it.

No, you cannot. That is an illogical jump that you keep incorrectly trying to make. There is no system or combination of systems you can define that allow this statement.

In a similar manner to yesterday's case, "the force I applied to the string" corresponds to "the force I applied to the spring," and the object certainly moves, so why is it that when connected to a spring, the work done is zero?

Be systematic and go step by step. What are your system(s)?

You are getting confused because of two things you keep doing. One is not clearly identifying your system(s). The second is making statements that are not supported by the analysis. You need to be more careful in both your choice of system and in your resulting statements.

 

[John Constantine]

No, you cannot. That is an illogical jump that you keep incorrectly trying to make. There is no system or combination of systems you can define that allow this statement.

I understand now that only the force directly applied to the system can do work on the system. When I pull the system consisting of the string and the object through the string, strictly speaking, I am only doing work on the string and the object as a whole, not directly on the object. I am Korean, and many people tend to ignore the string when asked to find 'the work I did on the object' in such problems. Strictly speaking, the work I did on the object is zero, but since the string has no mass and only serves to transmit my force, we skip this logic. If the string has no mass, the work done is the same whether I pull the object directly or through the string, as long as the force and distance are the same. These omissions confuse me. I have learned that setting up the system is fundamental. Thank you very much.

 

[Mister T]

TL;DR Summary: Work and Energy Consumption

According to the law of conservation of energy, I would lose 10J of energy, and the object would gain 10J of energy

Not necessarily. The object may not gain 10 J of energy. It might gain only 5 J of energy, and the internal energy of the block's environment gains 5 J, which shows up as an increase in temperature.

The law of conservation of energy is a generalization that includes both mechanical and thermal interactions.