Trying to understand power/work

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The discussion centers on the relationship between power, work, and acceleration in vehicles, particularly tractors and cars. It highlights that while a tractor with double the power can pull the same load at twice the speed, the acceleration of a vehicle is more complex due to the kinetic energy equation, which involves the square of velocity. It is noted that to double the rate of acceleration for a constant mass, four times the power is required, not just double. The confusion arises when considering whether a car with double the power can accelerate from 0 to 60 m/s in half the time, as this would necessitate greater force. Overall, the conversation emphasizes the intricacies of power dynamics in horizontal motion compared to vertical lifting.
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you see a lot of reference to the fact that a forklift or winch or something with "twice" the power of a another one can lift twice the mass in the same time, or the same mass in half the time, etc. This makes sense.

Power in the horizontal direction makes less sense to me. If a tractor has twice the power it can similarly do twice the work in the same time, but can it pull the same mass from point A to B in half the time? If you look at power as KEf-KEi/t, it would appear that it can't because velocity is squared in the KE equation (KE = 1/2mv^2).

Can someone help me clarify this?
 
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southernson said:
you see a lot of reference to the fact that a forklift or winch or something with "twice" the power of a another one can lift twice the mass in the same time, or the same mass in half the time, etc. This makes sense.

Power in the horizontal direction makes less sense to me. If a tractor has twice the power it can similarly do twice the work in the same time, but can it pull the same mass from point A to B in half the time? If you look at power as KEf-KEi/t, it would appear that it can't because velocity is squared in the KE equation (KE = 1/2mv^2).

Can someone help me clarify this?

Well, tractors don't pull at the same power regardless of speed. But if they they did then I guess the velocity of the tractor would increase quadratically (assuming no friction).
 
Tractors are normally pulling against a constant load, not acceleration. Power equals force times speed, so a tractor with double the power will be able to pull the same load (tension force) at twice the speed.

In the case of acceleration with a constant mass, since the change in energy is relative to 1/2 m V^2, then twice the power only increases the rate of acceleration by SQRT(2) (with the same mass), and it takes 4 times the power to double the rate of acceleration (or think of 4 times the power as twice as much force at twice as much speed with constant acceleration).
 
Sorry guys, I'm still confused. Let's use a different example. Say just a car with an engine of power P and another with a power of 2P. If the first can go 0 to 60m/s in 20 seconds can the second to it in 10 seconds? If so, this can only happen by the second engine causing a faster acceleartion. How is that going to happen without a greater force?
 

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