Conservation of Momentum & Energy

Conservation of Momentum & Energy

Equation

p = mv

2.9

Equation

Ft = p

2.10

Momentum

Mass in motion. If an object has mass and it moves, then it has momentum. Momentum (little p; capital P stands for pressure) can be expressed as:

momentum = mass x velocity
p = mv

Notice that if either the mass or the velocity is 0, then the momentum is 0. Because momentum is conserved, p is a constant so that if one changes the other will automatically adjust to ensure that the product remains the same. If the mass increases by three times, then the velocity will automatically decrease to one third its previous value so the momentum is unchanged. This assumes that no external forces are applied.

Because momentum has a velocity term in it, it is a vector quantity and the velocity vector defines the direction of the momentum. Notice also that the equation for momentum is similar to the equation for kinetic energy. Both energy and momentum are conserved in a closed system.

Another way to express momentum is as a function of force. You will recall Newton’s famous force equation (Equ. 1.18):

F = ma

Acceleration is just the change in velocity over time. So, if initial velocity is 0, we can substitute v/t for a, and then p for mv:

F = m(v/t) = (mv)/t = p/t

Finally, cross-multiply the t to get:

force x time = momentum
Ft = p

The longer you apply a force to an object, the greater the velocity it attains and thus the greater momentum it has.

Note: If you’re wondering why “p” stands for momentum, here’s an occasion when studying Latin pays off. The p likely comes from “impetus” (to go towards or rush upon), which in Latin is petere.