What is force? How does a constant force output a nonconstant power?

Question

For a constant force, P=Fv. I understand the mathematical derivation of this, but this seems to me, intuitively, to be nonsense. I feel that my discomfort with this comes from a fundamental misunderstanding of force and Newton's Second Law, so I'm not really looking for any mathematical explanation. So, to begin: How is it that a constant force does not add energy to a system at a fixed rate? Consider a rocket burning a fuel at a constant rate. The chemical potential energy should be converted to kinetic energy at a constant rate, that is, 1/2mv^2 should be increase linearly. The magnitude of the velocity of the rocket would then increase at a less than linear rate, implying a nonconstant acceleration and therefore, a nonconstant force/thrust (F=ma). If force is indeed a "push or a pull," shouldn't that constant rate of burning of fuel yield a constant "push or pull" as well? Clearly not, so I would have to think that, somehow, a given force applied to a certain object at rest would in some way be different than that a force of the same magnitude being applied to that same object in motion. In this sense, is force merely a mathematical construct? What does it tangibly mean, in physical terms? Would a given force acting upon me "feel" differently to me (in terms of tug) as I am moving at differing velocities? Force being defined as a "push or pull," which is how it has been taught in my high school class, seems rather "handwavy," and maybe that's the issue. It's been troubling me for a couple of weeks and my teacher hasn't really been able to help, so thanks!

Answer 1

Mark's answer about forces is right on. Newton's first law,of motion sets out what a force is, directly:

"An object will remain at rest, or in motion at constant velocity, unless acted on by an unbalanced force."

A force (which is not balanced out by another; in other word, a NET force) changes velocity. If the velocity of an object changes, a force must be acting on it. If no unbalanced for is acting, velocity will not change. Newton's second law of motion says how the force affects velocity (in other words, how it is related to acceleration).

If the object's velocity does not change, Newton's laws say the acceleration is 0, and do not distinguish between whether it is 0 because the object is at rest, or in motion at constant velocity. This means that, if a net force is applied to a system which previously had a = 0, the experience of that force will be the same whether the system is at rest or in motion at constant velocity,

In the example you propose, you specify a constant rate of change in kinetic energy. I don't think this is particularly realistic for the given situation (since it would require all the work-producing forces in the situation of rocket propulsion to be conservative), but we can specify that. In that case, for reasons we can go into if you like, you end up with a speed-dependent force; specifically, a force inversely related to speed. Speed-dependent forces are not in any way forbidden (in fact, one of them, drag, often comes up in fundamental classes). But that is the reason the force magnitude changes over the flight: because of the kinetic energy condition, not because the force is somehow being fundamentally different.

Also, there is no fundamental reason to expect a constant force if energy consumption is constant.

If you have any further questions about any of that, please feel free to ask,

Answer 2

My answer is simply "back to basics"....

Force is what causes things to change their inertial state. F = m*a tells us that the application of a force will cause a change in velocity and therefor a change in momentum.

Force acting through a distance is work. Same answer if the calculation is done based on the change in velocity. In either case, work is used to change the energy state.

Finally, power is the rate of doing work.

Answer 3

Consider systems of variable mass. A rocket burns fuel and ejects mass downward so the system( fuel + rocket) is changing this creates thrust. Does that help?

Jim