The Crashing Dragster: Conservation of Momentum

The last time we discussed our uncle Jim’s Corvette going really quickly at the drag strip. We calculated using the straight-line motion equations that the car at the end of the drag strip was going about 137 mph. We also learned that his rate of change of velocity is called acceleration.

The next thing we’re going to learn today is about how uncle Jim’s car at the end of the drag strip suddenly hit a deer and caused the deer to go flying in one direction. Uncle Jim’s car you can well guess got smashed up real bad, rolled over and stopped at the end of the drag strip in a pile of debris and smoke. Uncle Jim was okay, but the deer wasn’t.

What happened here was a momentum exchange.

The Corvette was going 137 mph and imparted some of its motion into the deer which went was catapulted away from sight. Uncle Jim’s car felt the effects, flipped and slowed down with some major frontal jam. Uncle Jim, he was okay, the car was okay but the deer didn’t fare so well.

What we want to examine today is:

What is momentum?
What does momentum have to do with go karting or Jim’s drag racer?

As we discussed last time velocity is the distance covered by an object over a period of time. When you tag on a piece of mass to a velocity or multiply the mass times the magnitude of the resulting quantity is called momentum. In other words mass * velocity = the total momentum.

Momentum is important to us because it is neither eaten up or destroyed. When something hits something else it’s overall momentum of the system is transferred to something else.

The classic example of momentum is a pool table. We’ve seen billiard balls that hit one another and bounce around the table. However, what is happening is an exchange of momentum or an exchange of what we would normally call energies. (But we don’t want to jump ship and start talking about energy because that is on the next level beyond momentum. It is the integration of momentum changes…Ooookay….yeah lets not get carried away here!)

But what is important here is that momentum is a quantity or a magnitude of measurement which will be very useful in calculating forces later. When a billiard ball hits another billiard ball very often what occurs is that the white billiard ball (which is the cue ball) hits the eight ball. The eight ball suddenly starts going the speed that the cue ball was going. The cue ball stops completely while the eight ball goes flying.

What has occurred here is a transfer of momentum. The cue ball weighs mass-1 and so does the eight ball, it weighs the same mass-1. So when the cue ball hits the eight ball the overall equation is as follows:

Momentum cue ball plus moment eight ball initial equals moment cue ball final plus moment am eight ball final. (Right….!??) Let’s break it down…

For our calculations the following variables will be used:

P = momentum
Vi= velocity initial (starting)
Vf= velocity final
m = mass

mVi cue ball + mVi eight ball = mVf cue ball + mVf eight ball

m=300grams

Vi Cue Ball = 10 m/s
Vf Cue Ball = 0 m/s

Vi Eight Ball = 0 m/s
Vf Eight Ball = 10 m/s

We will do a little algebraic manipulation and by default the “m’s” or the masses cancel out in the equation so the resulting equation looks as follows:

V cue ball + V eight ball = Vf cue ball + Vf eight ball

As we can see the velocity of the cue ball in the initial state was a certain speed of 10 m/s and the velocity of the eight ball was 10 m/s in the final outcome. The velocity final for the cue ball is zero therefore the equation would look as follows:

Vi cue ball = Vf eight ball

What we have just described here is an exchange of momentum. All are trying to learn here is the idea of momentum and that it is a mass times velocity equals moment, or:

Momentum = Mass * Velocity

Now are going to talk momentum as it changes. The best way to look at that is uncle Jim’s car start at 0 mph but it ended up going 137 mph in 13 seconds. We know that the acceleration equals some number. We are going to look at uncle Jim’s car abstractly:

Uncle Jim’s car has a mass M. and it has a velocity initial of zero and the velocity final 137 mph.

(We made a statement about the conservation of momentum. Momentum is neither created nor destroyed. The action of the gasoline combusting imparting energy and so forth into the pistons, a crankshaft, transmission, into the drive line, through the tires and then propelling the car forward is converting chemical energy into another form of energy called mechanical energy; therefore, the momentum of the molecules and so forth was not destroyed was just transferred.)

So the equation for Jim’s car is as follows:

Mvi – Mvf/ Delta Time = change in momentum/Time

If we take a look at the change momentum we see that we have a change of velocity over a period of time. And this change of velocity/time is known as acceleration. So what we can do with this equation is substituted acceleration for the velocity change and we have the following equation:

Change in momentum/Time = Mass *(Vf-Vi/Delta Time)

Or

Change in momentum/Time = Mass *Accelleration

Or you may be familiar with this formula 

F=Ma

We call this change of momentum force. In metric units we call it Newtons in English units we call it pounds.

Conclusion:

Momentum = mass *velocity. The change in momentum per unit time is force. The change in momentum is characterized by a mass changing in velocity or speed, and because we live in a dynamic world, everything happens over time.

Whenever we see vehicle start from one position and move to another position, a force is pushing on it. It is also characterized by a change in velocity.

If the vehicle is moving at a constant speed and nothing is holding it back then there is no change in momentum and therefore there is no force actually acting on any vehicle.

In layman’s terms we call this coasting, and quite really we are not adding any energy or force to the system. When we ride the bike really hard and then stop peddling we are coasting and not adding any more force to the pedals. Therefore, there is no change in velocity occurring at that point in time, and therefore no force other than the wind and the bearings and so forth acting to slow (change velocity) the bike.

So again the concepts that should have been learned today would be momentum and its conservation: that it is neither created nor destroyed and secondly that the change of momentum is known as force.

Force is vthe most valuable contribution to our sciences in that stresses and horse powers and so forth can be calculated knowing this quantity.

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