Machine elements engineering question

From Newtonian physics, F = ma, the net force of a system will contribute to its acceleration, and in a case of no friction or such energy losses, theoretically all forces will contribute to acceleration in that sense.

In the context of machine elements, if we ignore friction and everything... all torques added to a gear will contribute to its acceleration, described by the formula T = I*angular_acceleration

From what I understand, the relation between power, force and speed is: P = F*v
The dimensions make sense, but I've seen this formula used in such a way:
Pmotor = Fmotor * v

And I don't now how to connect this to the acceleration concept.
If Fmotor contributes to acceleration, why does P = F*v even exist, it relates the force and speed directly, but if I waited a little longer while keeping that same force the speed will increase correct?
Or maybe this formula is the force it takes to maintain the speed v, which makes sense, and so it would be equal to the friction and other forces of loss correct? Is that what it is?

If that's what it:
Does that mean it doesn't apply for ideal scenarios without friction and resistance?
Why does the power P or v even matter in such a case, wouldn't a formula such as Fmotor = F_friction be better? Cause the speed wouldn't matter in such a case since as long as Fmotor = Ffriction it will always be maintained, so I don't get why P = F * v is even used.

Perhaps I don't understand the concept or what this formula describes. Any explanation is appreciated, thank you for your time.

Reply 1

mnot

Universities Forum Helper

Original post by anatino

From Newtonian physics, F = ma, the net force of a system will contribute to its acceleration, and in a case of no friction or such energy losses, theoretically all forces will contribute to acceleration in that sense.
In the context of machine elements, if we ignore friction and everything... all torques added to a gear will contribute to its acceleration, described by the formula T = I*angular_acceleration
From what I understand, the relation between power, force and speed is: P = F*v
The dimensions make sense, but I've seen this formula used in such a way:
Pmotor = Fmotor * v
And I don't now how to connect this to the acceleration concept.
If Fmotor contributes to acceleration, why does P = F*v even exist, it relates the force and speed directly, but if I waited a little longer while keeping that same force the speed will increase correct?
Or maybe this formula is the force it takes to maintain the speed v, which makes sense, and so it would be equal to the friction and other forces of loss correct? Is that what it is?
If that's what it:
Does that mean it doesn't apply for ideal scenarios without friction and resistance?
Why does the power P or v even matter in such a case, wouldn't a formula such as Fmotor = F_friction be better? Cause the speed wouldn't matter in such a case since as long as Fmotor = Ffriction it will always be maintained, so I don't get why P = F * v is even used.
Perhaps I don't understand the concept or what this formula describes. Any explanation is appreciated, thank you for your time.

Power is the rate of energy use relative to time, force is the work exerted over a distance, on an object and energy is the ability to do work, all three are different and important in physics and engineering. It’s typically about identifying the right measurable for the right problem.

I would say in most applications you probably would be interested in either force or power & probably not both, there certainly are times you may use both typically this is with managing complex systems & you would try and choose one to optimize around. It just depends on the context although environment you’re working. Adding to add more confusion to this there are similar variables by pressure which you could align to engineering around the same system.

The challenges you are working on textbook style work problem. This is designed to make you think about the theory, but not actually a practical way of how you use it, in reality you would have a problem derived from a potentially complex system you’re working on you would then distill this down into one of the core variables that you could work against and you would define the problem into sets of inputs, boundary conditions, assumptions, and outputs, from this the variables most suitable to work with for you and potentially for your operators for the rates can be leveraged for whatever method you use to “engineer against” from a first principles calculation, or using complex high fidelity physics tools or whether you were using a physical experiment.