# NavList:

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

**Re: Definition: Force vs Power**

**From:**Bill Noyce

**Date:**2003 Apr 24, 10:42 -0400

> 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. > > Second, can these notions be expressed in a way that my uneducated brain can > grasp? Some basic physics definitions: Momentum is defined as Mass x Velocity. It has magnitude, and also direction (since Velocity has direction). Force is defined as Mass x Acceleration. It represents how hard you are pushing (or pulling) on something, and can be measured with a spring. It has magnitude and direction. Note that Acceleration is (change in Velocity)/Time. Thus, Force represents the rate of change of Momentum. Energy is defined as Mass x (Velocity squared). It has magnitude, but no direction. Note that Energy could also be defined as Momentum * Velocity -- it's the same thing. Power is the rate of change of Energy. So it can be defined as Momentum * (change in Velocity)/Time, and if you work it out, this is equivalent to Velocity * Force. Now, I've been a bit sloppy with the notation "*" here. It should actually represent a "vector dot" product. When you multiply two vectors (items with magnitude and direction), the result depends on the directions, as well as on the magnitudes. With a "vector dot" product, the result of A*B is mag(A)*mag(B)*cos(theta) where theta represents the angle between the vectors. So when multiplying a vector by itself (as when squaring velocity to get energy), the result is simply the square of the magnitude, since cos(0)=1. When multiplying two vectors that point in exact opposite directions, the result is the negative of the product of their magnitudes. And another important special case occurs when the two vectors are at right angles: the vector dot product is zero, regardless of the magnitudes, since cos(90d)=0. Imagine a ball on the end of a rope, tied to a tall pole. Stretch out the rope, and give the ball a push, so it rotates around the pole. The rope is exerting a force on the ball, as it is constantly changing (the direction of) the ball's velocity vector. But no power is expended, since the direction of the force is always perpendicular to the direction of the velocity vector. Hope this forms a useful starting point... -- Bill