Is Energy Being Conserved in This Almost Paradox Scenario?

[BrettD]

Imagine a 100N block rising at a constant velocity with a 100N force in the vertical direction pulling it, and 100N of gravity pulling it down. The net force on the block is 0, so work, force time displacement, is also 0. However, the block is rising and clearly gaining gravitational potential energy. How is this possible?

 

[rtsswmdktbmhw]

The block doesn't lift itself. In other words, it's not doing the work to increase its own potential energy.

 

[russ_watters]

Imagine a 100N block rising at a constant velocity with a 100N force in the vertical direction pulling it, and 100N of gravity pulling it down. The net force on the block is 0, so work, force time displacement, is also 0. However, the block is rising and clearly gaining gravitational potential energy. How is this possible?

Welcome to PF!

That's not what net force is for. The force applied to the block does work. The force of gravity absorbs that work in the form of gravitational potential energy.

 

[BrettD]

What would the work done on the block be over x meters? Isn't the net force equal to mass times acceleration, which in this case is 0?

 

[russ_watters]

What would the work done on the block be over x meters? Isn't the net force equal to mass times acceleration, which in this case is 0?

Yes, but again, net force isn't part of what you are asking. The work done is applied force times distance.

 

[sophiecentaur]

Don't confuse Force with Energy. There is a constant force (gravity) acting all the time. If you throw it up, it will gradually slow down as the Kinetic Energy it started with changes to Potential (weight times the distance it rises) At the maximum height, the KE is all used up.
If you use a motor to raise it, the upwards force will be the same as the weight and the work done will be mgh. (Assume, for a start, it is all done very slowly and that you can ignore any kinetic energy but a real situation - like a lift / elevator will involve a speeding up and slowing down at the ends of the trip so the forces will not be constant.

 

[BrettD]

In a physics problem like similar to the block, where the acceleration was always near zero, my physics teacher said that no work was done because there was no acceleration, and the work from gravity canceled out the work done by the upwards force.

 

[rtsswmdktbmhw]

What would the work done on the block be over x meters? Isn't the net force equal to mass times acceleration, which in this case is 0?

The net force you exert in lifting the block is equal to mg=100N up, and net force times distance h is mgh. As previously said, the block doesn't lift itself so it doesn't make sense to take the net force on the block. The work done by the block is ziltch, the work done by you in the lifting the block is what increases its potential energy.

In a physics problem like similar to the block, where the acceleration was always near zero, my physics teacher said that no work was done because there was no acceleration, and the work from gravity canceled out the work done by the upwards force.

What are the details of the similar problem?

 

[BrettD]

Regarding the question "What is the total work done on Throcky by all forces?" I originally thought it would be the change in mgh, but my Physics teacher said that because he's in equilibrium between the force F and gravity, net force on him is 0, and so is work.

 

[russ_watters]

Regarding the question "What is the total work done on Throcky by all forces?" I originally thought it would be the change in mgh, but my Physics teacher said that because he's in equilibrium between the force F and gravity, net force on him is 0, and so is work.

The question asks for the total work done by all forces. Not a very common way of asking such a question, but in general, conservation of energy demands that the sum of works done by balanced forces must equal zero:

W(applied force) + W(gravity) = 0

But in your first example, you seemed confused about how the block can gain potential energy. Potential energy is the other work. So you seemed to be asking a different question.

The difference is whether you are asked to find one work, the other work or the sum of both.

 

[BrettD]

Wouldn't the total work done on the block be the same as the sum of the work done by each force?

Edit: ...and the total work done should be mgh, right?

 

[russ_watters]

Wouldn't the total work done on the block be the same as the sum of the work done by each force?

Yes.

Edit: ...and the total work done should be mgh, right?

No, as you said the total work is zero.

I'm not sure what the issue is here. You see that there are two forces being applied to the block, right? Do you see that the forces point in opposite directions? Do you see that asking about the total work is different from asking about the work done by the upward force?

 

[BrettD]

The issue is that I think these things:
1)Change in the block's potential energy is the total work done on the block (Assuming no changes in other forms of energy)
2)Total work done on the block is 0
3)Change in potential energy is mgh

Clearly, if 2 and 3 are true, the first can not.

 

[russ_watters]

The issue is that I think these things:
1)Change in the block's potential energy is the total work done on the block (Assuming no changes in other forms of energy)
2)Total work done on the block is 0
3)Change in potential energy is mgh

Clearly, if 2 and 3 are true, the first can not.

Right: #1 is not correct.

 

[BrettD]

Would it be correct to think of there being two types of forces, A) ones that add energy to a system and B) ones that do not add energy to a system?

In the block example, the outside force is type A and gravity is type B. Statement 1) could be changed to: 1)Change in the block's potential energy is the total work done of the block by type A forces (assuming no changes in other forms of energy)

 

[russ_watters]

Would it be correct to think of there being two types of forces, A) ones that add energy to a system and B) ones that do not add energy to a system?

Now you're asking about a 3rd separate issue ("the system") before apparently understanding either of the first two. It isn't useful here and you should avoid discussing "the system" until you first understand the other issues you were asking about.

Perhaps it would help if I asked you some questions:
1. What is the work done on the block by the applied force?
2. What is the work done on the block by gravity?

 

[BrettD]

Doesn't gravity just transform potential energy into kinetic energy, or vice versa?

 

[russ_watters]

Doesn't gravity just transform potential energy into kinetic energy, or vice versa?

In the problem you gave us, it didn't.

 

[BrettD]

Couldn't you imagine the force as adding kinetic energy to the block as gravity changes that energy to potential energy at the same rate? Would taht be a valid interpretation?

 

[russ_watters]

Couldn't you imagine the force as adding kinetic energy to the block as gravity changes that energy to potential energy at the same rate? Would taht be a valid interpretation?

No, it really isn't. If the speed is constant, it is constant.

 

[sophiecentaur]

Couldn't you imagine the force as adding kinetic energy to the block as gravity changes that energy to potential energy at the same rate? Would taht be a valid interpretation?

I think it could be more useful for you to come up with an actual scenario and then see if this 'almost paradox' you are thinking of, still applies. If you work out, accurately, the energy and work situation at all times you get the Energy being conserved. At the moment, you seem to be looking for something that's not there.