Quote:
Originally Posted by jyl
Help me understand a physics concept. I don't get the intuition behind it.
It has to do with power.
I'll ask my question in the context of a pulley problem.
A block of mass M1 is on a frictionless plane, inclined at angle Z. A string is fastened to that block. The string passes over a frictionless pulley. The other end of the string is fastened to a hanging block of mass M2.
The force of gravity on block 2 is F2 = M2 x g. The component of the force of gravity on block 1 that is tangent to the plane is F1 = M1 x g x sin Z.
If M2 > M1 x sin Z, then block 2 will descend and pull block 1 up the inclined plane. The blocks will accelerate at A = [ (M2 - M1 * sin Z) / (M1 + M2) ] * g although mathematically block 1 has acceleration A and block 2 has acceleration -A. The blocks will have the same scalar component of velocity V.
Assuming the blocks start at rest, at time T, velocity V = A * T.
(Please correct me if I have it wrong so far. This is straight out of first year physics but college was a long time ago.)
I'm trying to calculate the power that block 2 applies to block 1. Block 2 is applying a constant force F2 = M2 * g to block 1. Power = force x velocity. So Power P = F2 x V.
(Still right?)
Now, this is what I don't intuitively get. As T increases, with constant A, velocity increases. That means power P increases. At T = 0. P = 0. The faster the masses move, the higher the power that is being applied to block 1.
If the force remains constant, how can power increase?
I don't understand this intuitively.
Actually, I always have trouble intuitively understanding power. I recall vaguely that in physics class, we always calculated Work, and then divided by time to get Power. We didn't start by calculating Power. Maybe that's why I never really got comfortable with Power.
Using that approach, I can see that block 2's kinetic energy increases at a doubly accelerating rate, so that in the 1 second interval from T = 1 to 2 there is a small increase in KE, while in the 1 second interval from T = 10 to 11 there is a much larger increase in KE. So if P = KE / T, the power in the first interval is small while the power in the second interval is much larger. But I don't "get it".
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maybe if you see another example, which is even more counter
intuitive because the force is going down while the power is going up.
here are the Torque and HP curves for a popular 911 motor
torque is the angular analog of force applied in your example and power of course is the analog of power in your example and rpm is the analog of linear velocity in your example
Note that the torque(force) is
decreasing from ~5k rpm yet the power is increasing from that point to ~6200rpm. Why? because the hp is the
product in the mathmatical sense of the decreasing force(torque) and increasing rate(rpm)
BTW there are many concepts in Physics that go against intuition, among the most bizarre at the macro scale is exhibited by a simple toy, a spinning top.