Physics Notes - Dynamics

Deriving the Work/Energy Equation

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

Net Force on an Airplane Diagram

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. If the object's initial velocity was vo and its final velocity is v, kinematics tells us that:

v squared = v sub 0 squared etc.

Multiplying both sides of this equation by the object's mass, m, gives:

m times v squared, etc.

Rearranging:

2 m a delta x = etc.

Since Fnet = ma (Newton's Second Law), we can substitute:

2 Fnet delta x = etc.

then divide both sides of the equation by 2:

Fnet delta x = etc.

This is the Work/Energy Equation. Alternatively, here is an alternate derivation similar to the text's (p. 109).

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last update November 14, 2007 by JL Stanbrough