# Work – Constant Force, and Changing Force

Published on: Fri Mar 12 2010

Work increases or decreases over displacement.
1. Kinetic Energy equals one half mass times velocity squared
2. Work equals change in Kinetic Energy, which is equivalent to final kinetic energy minus initial kinetic energy.
3. Work equals force over displacement (If the force and displacement are parallel).
4. Work equals Force over displacement times cos theta (If the force and displacement are at an angle to each other. Theta is the angle formed from Force and displacement).
Force is an example of a Dot Product or Scalar Product of two vectors, for example vector’s A and B.
1. Vector A dot product Vector B is equal to the scalar value of magnitude A times magnitude B times cos theta.
2. Work (scalar value) equals the dot product of Force times displacement, which is equal to magnitude of Force times magnitude of displacement times cos Theta.
3. Dot Products distribute.
So the point of learning about dot products is that work, can be broken down into it’s component parts, Fx, Fy, Fz and dx, dy, dz and you can use these component parts to find out the angle theta. If we think about a spring and the work done to pull a spring open, the Force needed to continue pulling the spring grows, the further you pull on the spring This makes the Force Applied equal to a constant “k” times displacement x.