You have probably discussed momentum in an earlier physics course. Momentum is a combination of the mass of a body and its velocity, just like kinetic energy. There are two main differences between KE and momentum, however.
That means that there are really three quantities involved in the calculation of momentum, not just one.
If, for some reason, we wanted to convert a momentum-like quantity into an energy-like quantity, we would have to multiply by a velocity-like quantity:
Let's do a few simple examples.
Q: I toss a rubber ball of mass m = 0.2 kg gently to the East at v = 5 m/s. What is the ball's momentum? Q: Crazy Ellie fires a 125-grain cartridge from her Smith and Wesson .357 Magnum handgun (one grain is approx 0.065 grams). The bullet leaves the muzzle of the gun at v = 440 m/s towards the East. What is the bullet's momentum?
Why bother with momentum? One of the main reasons is that when objects collide or interact, then -- as long as there are no significant external forces -- the initial momentum of the system is the same as the final momentum.
Be careful: this applies to the sum over all the objects involved, not each object individually. In other words,
In fact, this equality must apply to each component of the vector momentum, so we could also write an equation for each component separately. I'll use subscripts i to mean "initial" and f to mean "final".
You may recall that when I discussed kinetic energy, I was careful to add lots of qualifiers to the statement "kinetic energy is SOMETIMES conserved in interactions between particles." It was only collisions between hard, compact balls -- the "elastic" collisions -- in which KE was conserved. For example, in this collision between two cars (click on the first picture for a very large movie), KE is definitely NOT conserved:
On the other hand, the total momentum of this pair of cars IS conserved:
Let's work through a few simple examples of momentum in the non-relativistic regime, just to see how it can be used in practice.
A car of mass m1 = 2000 kg moving at vi = 20 m/s slams into a stationary truck of mass m2 = 15,000 kg. Immediately after they collide, what is the speed with which the combined wreckage slides forward?
Which of the following is the final velocity vf?
A car of mass m1 = 2000 kg rolling slowly at vi = 5 m/s bumps into a stationary truck of mass m2 = 15,000 kg. Afterwards, the car moves backwards with velocity v1f, and the truck creeps forward at v2f.
Which of the following are the final velocities?
A car of mass m1 = 2000 kg is driving at v1i = 20 m/s due East as it enters an intersection. A minivan of mass m2 = 6000 kg going v2i = 30 m/s drives into the intersection along a road which runs θ = 30 degrees South of West. The meet in a most unhappy fashion.
Which of the following is the final velocity of the combined wreckage?
If the angle α is drawn as shown, how large is it?
An invariant quantity is one that has the same value, no matter which observer is making measurements. The space-time interval
is an example of an invariant quantity.
Is kinetic energy an invariant quantity? Let's find out.
The Blue Man throws a ball (m = 0.2 kg ) at a speed of v = 20 m/s to the right.
Q: What is the momentum of the ball, according to the Blue Man?
But the Blue Man and the ball are all travelling across the landscape at a speed of w = 50 m/s to the right, as measured by the Red Men.
Q: What is the momentum of the ball, as measured by the Red Men?
Copyright © Michael Richmond. This work is licensed under a Creative Commons License.