# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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@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 Science Serving the Fisheries http://home.istar.ca/~gadus