Violation of energy conservation law?

[Gadersd]

There are two disks of the same size and mass. A 5N force acts through the center of the first and another 5N force acts through the bottom of the other. The forces both point to the right. According to what I have learned, the linear momentum of both objects will be the same, but the second one will have angular momentum. The second object must then have more energy than the first. How can two equal forces have different energy outputs?

 

[jbriggs444]

If the two forces produce the same change in linear momentum then they must act for the same duration. But the force on the bottom of the disk is acting over a longer distance -- not only is the disk moving linearly, it is also rotating. A force that acts over a longer distance does more work and imparts more energy.

 

[Gadersd]

I am having a difficult time wrapping my head around this. If push my hand on the two disks with equal amount of force for 1 second the second one would not be any more difficult to push, yet I am putting more energy into it.

 

[A.T.]

would not be any more difficult to push, yet I am putting more energy into it.

What does "difficult to push" mean? Force? Energy is not force, that's why it has a different name.

 

[Gadersd]

The second would not require any more force so it would not be any more difficult to push.

 

[A.T.]

The second would not require any more force so it would not be any more difficult to push.

Depends on the definition of "difficult to push".

 

[Gadersd]

The second object would not tire my arms any more than the first since the duration and extent of the forces are the same.

 

[Dale]

Yes, it would tire your arms more. You would have to move your arms faster. Going faster with the same force is more tiring.

 

[A.T.]

... tire my arms ...

That is a very complex definition, based on a inconsistently efficient machine: the human body. There is no simple relation between you feeling tired and the force, energy you impart on other objects.

 

[Gadersd]

Wouldn't moving my arms faster output more force?

 

[A.T.]

Wouldn't moving my arms faster output more force?

You specified that the forces are the same.

 

[Gadersd]

Yes, the forces are the same, but if I moved my arms faster as DaleSpam suggested then that would output more force which violates my original question.

 

[A.T.]

if I moved my arms faster as DaleSpam suggested then that would output more force

He didn't suggest more force, just more tiring.

 

[Dale]

if I moved my arms faster as DaleSpam suggested then that would output more force

No it wouldn't. Force and speed are different things. You can have different forces applied at the same speed or the same force applied at different speeds.

 

[Gadersd]

Can you use mathematical proof to explain this. I understand claims better when they are in mathematical form.

 

[mfb]

E=F*d with the energy E, force F and the distance d - assuming a constant force in the direction of motion, otherwise we need an integral.
There is no mathematical proof as this is physics, not mathematics.

 

[Gadersd]

I have never heard of forces having speeds. Never in any of the lessons were speeds of forces mentioned.

 

[jbriggs444]

It is not the "speed of the force". It is the speed of the point on the object at which the force is being applied. The rate at which energy must be supplied (i.e. the "power") is equal to the vector dot product of force and the velocity of the point of application of the force.

 

[Dale]

Your arm Has a speed and your arm exerts a force. Do you recognize that those are independent.

 

[Gadersd]

The point on the bottom on the second disk is accelerating faster than the point on the first disk since it is rotating so I must move my hands faster to make up for the greater velocity. Is this correct?

 

[mfb]

Yes.

 

[Dale]

And doing so is tiring.

 

[A.T.]

And doing so is tiring.

That's true. But moving the arm is tiring even if it doesn't push anything. And it's also tiring to hold it up without moving. Therefore using arm tiring for measuring some external work to check energy conservation is just ridiculously overcomplicating things.

If the OP wants to have equal forces for equal time, just attach two identical rockets to your disc.

 

[jbriggs444]

No. Let us not use rockets. The intuition is that two rockets deliver equal energy when fired for an equal duration. The fact is that the power delivered by a rocket is proportional to the rocket's velocity. That just leaves us with one more thing to explain.

I think that we should use the law of the lever instead and explain the relationship between "work" (force times distance) and "energy".

Gadersd... Can you agree that the energy it takes to lift an object is proportional to the weight of that object times the height to which it is raised?

 

[CWatters]

The second would not require any more force so it would not be any more difficult to push.

So if I ask you to push my car you won't ask how far because it's no more difficult or tiring to push it one mile or ten miles :-)

 

[James Demers]

The second object must then have more energy than the first. How can two equal forces have different energy outputs?

mfb gave the answer, in the equation E=Fd (energy E, force F and distance d).

You're expending more energy on one disk than on the other, even if you're applying equal force. That disk then will have more kinetic energy. (And that arm will be more tired.)