Force/torque in a differential / gear ring.

[hihiip201]

Hi guys:



I have 3 questions:


Imagine an open differential that looks like a gear ring :

and now let's call the rings (orbital gear) the wheel gear, the gear in the center the center gear.


1. is the reason why torque from input shaft is evenly split to both wheels regardless of different speed because : As long as the speed difference is constant, the differential has a constant angular velocity and hence net torque must equal to zero?



2. In the gear ring video, if i am to apply a torque not from the differential(center gear in track/sun gear) but now either : hold one of the wheel ring(orbital gear) fixed and turn the other one, or if I turn both of them at the opposite direction.

will it be correct to say that under no friction, there will only be forces between the wheel ring and track gear be non-zero during acceleration? in other word if i continue to exert a force from one wheel ring I will be accelerating the angular speed and speed of the center gear? and just the angular acceleration if i turn both wheel ring together?



3. Finally, a more fundamental question:

why is horse power equal to force times velocity (or T omega)? is it because we first defined kinetic energy to be 1/2mv^2? What prompted the people in the old times to define energy in such a way?

thanks!

 

[sophiecentaur]

why is horse power equal to force times velocity

Power is work per unit time (Definition of power)
Work is force times distance
so
Power is force times distance per unit time
Distance per unit time is velocity
Re-grouping gives:
Power is force times velocity
QED

 

[hihiip201]

Power is work per unit time (Definition of power)
Work is force times distance
so
Power is force times distance per unit time
Distance per unit time is velocity
Re-grouping gives:
Power is force times velocity
QED

Oops sorry I think my question should have been why force is force times distance then.

I recognize that it was introduced by a French mathematician as weight lifted through a height, but how do we know that work, which was introduced in terms of potential energy works for kinetic energy as well?


thank you

 

[sophiecentaur]

Oops sorry I think my question should have been why force is force times distance then.

I recognize that it was introduced by a French mathematician as weight lifted through a height, but how do we know that work, which was introduced in terms of potential energy works for kinetic energy as well?


thank you

You don't mean that, do you? lol
'work = force times distance' ties directly with the Equations of motion, Newton's laws and the conservation of Energy
You do work by accelerating an object and that work turns up as KE - the sums all work.
Raise an object to a height of h and the work done is mgh . That is the GPE you have given the object. Drop it from that height and the KE at the bottom will be the same as the GPE at the top. "Where else could the energy go? - is the crucial question which justifies that step in reasoning.

 

[hihiip201]

You don't mean that, do you? lol
'work = force times distance' ties directly with the Equations of motion, Newton's laws and the conservation of Energy
You do work by accelerating an object and that work turns up as KE - the sums all work.
Raise an object to a height of h and the work done is mgh . That is the GPE you have given the object. Drop it from that height and the KE at the bottom will be the same as the GPE at the top. "Where else could the energy go? - is the crucial question which justifies that step in reasoning.

ya i didn't mean "that" lol, fail.
when you say gpe is converted into KE when dropped, aren't we still using the work energy theorem in that case? I'm trying to understand how that theorem is coming from in the first place.

I can see how kinetic energy and work can tie together via GPE, but there's got to be some physics reasoning to justify using work energy purely on kinetic energy.

thank you for your reply!

 

[sophiecentaur]

The "physics reasoning" is that Energy is conserved. If you can't come up with somewhere else the energy can go, all the GPE must 'go into' the resulting KE. Once it gets back down to the ground there is no GPE left. Are you suggesting there should be (even in our ideal case) some other form of energy in the resulting situation? Would that make sense?

It is an article of faith that energy in = energy out but better than that, as it is confirmed by experiment many times. Sometimes the energy is hard to identify (e.g. experimental error or the dreaded E = mc². You never get more energy out than you would have expected, if you did the budget correctly.

I don't know what more you could want. Sorry. You may just have to live with this and it will hit you as reasonable, eventually.

 

[hihiip201]

The "physics reasoning" is that Energy is conserved. If you can't come up with somewhere else the energy can go, all the GPE must 'go into' the resulting KE. Once it gets back down to the ground there is no GPE left. Are you suggesting there should be (even in our ideal case) some other form of energy in the resulting situation? Would that make sense?

It is an article of faith that energy in = energy out but better than that, as it is confirmed by experiment many times. Sometimes the energy is hard to identify (e.g. experimental error or the dreaded E = mc². You never get more energy out than you would have expected, if you did the budget correctly.

I don't know what more you could want. Sorry. You may just have to live with this and it will hit you as reasonable, eventually.

believe or not I know how stubborn I am, and I completely understand the concept of COE and the fact that it is proven by experiment, but I always just thought there are some other ways that you can look at it. instead of just saying "Oh,conservation of energy", It is reasonable to me, but I just don't feel like it is enough.