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M2 Power concept

If a force of constant magnitude is applied to some object, say a ball falling through the air or any scenario with a constant resultant force, then the object will be constantly accelerating, it will get faster.

If I slowly decrease the resultant force, never further than zero, it will eventually get to zero acceleration and maintain a maximum speed.


I am struggling a little bit with the power concept in M2. I wrote the above in an attempt to make contradicting or problematic analogy/example, but I understand that.

Still I don't see why one would have to decrease the force. If something gets faster and faster the more force I put in, why would I decrease it? I suppose the issue here is we are not dealing with a limitless supply of power, so I think this is my confusion. We can only work at a constant rate, never increasing our power output. But setting aside the power equation and just thinking logically, if something is at rest and in each second we are giving it X amount of energy, surely it will just get faster and faster and faster? A constant power output is a constant amount of energy given each second. If something is moving at a speed and we give it energy, it gains speed. Each second we are giving it energy, why would it ever stop increasing?
(edited 8 years ago)
Original post by TheFuture001
If a force of constant magnitude is applied to some object, say a ball falling through the air or any scenario with a constant resultant force, then the object will be constantly accelerating, it will get faster.

If I slowly decrease the resultant force, never further than zero, it will eventually get to zero acceleration and maintain a maximum speed.


I am struggling a little bit with the power concept in M2. I wrote the above in an attempt to make contradicting or problematic analogy/example, but I understand that.

Still I don't see why one would have to decrease the force. If something gets faster and faster the more force I put in, why would I decrease it? I suppose the issue here is we are not dealing with a limitless supply of power, so I think this is my confusion. We can only work at a constant rate, never increasing our power output. But setting aside the power equation and just thinking logically, if something is at rest and in each second we are giving it X amount of energy, surely it will just get faster and faster and faster? A constant power output is a constant amount of energy given each second. If something is moving at a speed and we give it energy, it gains speed. Each second we are giving it energy, why would it ever stop increasing?


Because the magnitude of resistive forces like air resistance is proportional to velocity. As a result of this, even though I am applying a constant force, the resultant force is decreasing since the magnitude of the resistive forces are increasing, until eventually your force is equal to the resistive force so there is no more acceleration.


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Original post by TheFuture001

Still I don't see why one would have to decrease the force. If something gets faster and faster the more force I put in, why would I decrease it? I suppose the issue here is we are not dealing with a limitless supply of power, so I think this is my confusion. We can only work at a constant rate, never increasing our power output. But setting aside the power equation and just thinking logically, if something is at rest and in each second we are giving it X amount of energy, surely it will just get faster and faster and faster? A constant power output is a constant amount of energy given each second. If something is moving at a speed and we give it energy, it gains speed. Each second we are giving it energy, why would it ever stop increasing?

The power is constant, but the velocity increases. Because p = Fv, the driving force must decrease. Certain types of resitive forces increase with velocity eg. air resistance..
If we denote resultant force by F, the driving force by d and the resistive force by r, we get the equation F = d - r. d is decreasing and r may be increasing depending on the situation. This means that F must decrease, so the acceleration decreases.

If there are no resistive forces, we can set up the differential equation mdvdt=pvm\dfrac{dv}{dt} = \frac{p}{v}, which has the solution v=2ptm+Av = \sqrt{\frac{2pt}{m} + A}. As you can see, the velocity increases forever, but the rate of increase slows with time. The velocity does not have an upper limit and tends to infinity as t tends to infinity.

If there are constant resistive forces, we get the differential equation mdvdt=pv−rm\dfrac{dv}{dt} = \frac{p}{v} - r. This does not have an easy solution but you can see that as v tends to p/r, the acceleration tends to zero, so there is a horizontal asymptote at v = p/r. As t tends to infinity, v tends to p/r.

You aren't considering the energy given out as heat.
Okay I think I see. The power equation supposedly considers the resistive forces increasing as velocity increases.

However the typical question states that (non-gravitational) resistive forces are constant and gives it a value. All that changes is the driving force. So we have a car being supplied energy from its motor/engine, the resistive forces are constant, yet the forward force exerted on the car declines. Is resistance due to air resistance implicitly implied?

Also another point, the equation implies that there is an infinitely huge force exerted on the object when it is at rest or just begins moving. I have a sense that this equation and the physics involved has less to do with the object and outward forces and more to do with how hard the motor/engine must work to get the object moving.

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