Dynamics Notes

Deriving the Work/Energy Equation - 2

A net force Fnet acts on an object through a distance delta x.

Net Force on an Airplane Diagram

This derivation follows the line of the one at the bottom of page 109 in the text, except that the text's assumes that the starting velocity of the object (and so its starting kinetic energy) is zero. You'll see why the author did that when you compare the derivations...

Suppose a constant net force Fnet acts on an object of mass m over some distance delta x. Newton's Second Law tells us that the object will have an acceleration a = Fnet/m, or:

Fnet = ma

It is a perfectly legal mathematical operation to multiply both sides of this equation by the distance the object moved, :

Fnet delta x = m a delta x

From kinematics, we know that:

delta x = v sub 0 t etc.

so substituting this into the previous result gives:

Fnet delta x = etc.

Since a = delta v over t and delta v = v minus v sub o, we can get:

Fnet delta x = etc.

removing parentheses:

Fnet delta x = etc.

and combining like terms gives the Work-Energy Equation:

Fnet delta x = etc.

last update May 18, 2000 by JL Stanbrough