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Re: Definition: Force vs Power
From: Trevor Kenchington
Date: 2003 Apr 24, 10:30 -0300

David Weilacher wrote:

> Recently, we were discussing effect of wind and current.  Actually, I believe we still are.
>
> It was suggested that Force = mass X velocity.  Also, that Power = velocity
squared.  (or is it mass X velocity X velocity?)
>
> First, is this stated properly by me.

No.

With my copy of the CRC Handbook of Chemistry and Physics open in front
of me (just to make sure that I have not forgotten everything of my
high-school physics!):

"Force" is defined as something that changes the motion of matter. A
boat floating without moving begins to move when a force is applied to
it. A moving boat slows down, speeds up and/or changes the direction of
its movement when a force is applied. Wind, prop discharge current, the
pull of a tow rope, wave drag acting on a moving hull and many, many
others can supply forces that alter the motion of the boat. (Of course,
everything is constantly subject to many forces so real-world motions,
as distinct from physical concepts, appear appear when the balance of
various forces changes. The forces of buoyancy and gravity, for example,
are usually far greater than other forces acting on boats but they
balance one another, at least as averages over reasonably short time
periods, and thus the motions we see are caused by the smaller forces
which act horizontally.)

Quantitatively, "Force" is equal to mass times acceleration, _not_ mass
times velocity. As Newton realized, a moving object will continue to
move in a straight line at constant speed unless acted on by some force
(which is why moving boats hit large static objects when their engines
fail to go astern at the right time!). In SI units, a force of one
Newton, if applied to a body with a mass of one kilogram, will
accelerate that body at a rate of one metre per second per second. That
is: For each second that the force is applied, the velocity of the body
will increase by one metre per second (all supposing, of course, that no
other force acts to resist the effect of the first one, whereas in the
real world motion generates friction which does directly oppose the
forces causing the motion).

When a force acts, energy is converted from some form (such as the
chemical energy in diesel fuel) into kinetic energy of the accelerated
object. (In the real world, that kinetic energy usually ends up as heat
when the moving object eventually gets slowed down again by friction.)
Again in SI units: When a force of one Newton acts through a distance of
one metre, one Joule of energy passes into kinetic energy.

Power is the rate of doing work, meaning the rate at which energy is
converted from one form to another. A power of one Watt means that one
Joule per second is being converted, thus a 100 Watt light bulb converts
100 Joules of electrical energy into heat and light every second.

So:

Power is energy per second but energy is force times distance, meaning:

Power is force multiplied by distance and divided by time, while force
acts to accelerate mass, thus:

Power is equal to mass multiplied by acceleration and distance, divided
by time. Unless I am muddling something, that means that:

Power is equal to mass multiplied by velocity and distance, divided by
time squared,

hence to mass multiplied by velocity squared, divided by time.

Which means that more power will allow a greater mass to reach higher
speeds in less time -- which matches exactly with the common-sense
notion of "power" in relation to engines and the movement of boats.

I hope that makes sense.

Trevor Kenchington

--
Trevor J. Kenchington PhD                         Gadus{at}iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

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