## Question:

I am in AP Physics as a junior in highschool, and i seem to be having an extremely hard time with some of the concepts they are teaching us. one in particular is linear momentum. I've only been taught it in the application of one object hitting another, but what about a problem such as a rocket and the force of the propelling gases on it? please help!!!!

## Answer:

To help you think about the rocket situation you mentioned in your email we need to talk a bit about cause and effect. The conservation of linear momentum is one of those things very near to the heart of what makes the universe work. For our purposes it is a cause, not an effect. That means we do not say linear momentum is conserved because... Rather we say this or that happens because linear momentum is conserved. If we take the conservation of linear momentum to be a "law of nature" then we can conclude all sorts of interesting things from that.

Suppose for example that we have a rocket loaded with fuel, initially at rest in our frame of reference. When we start the engines, some of the fuel is ejected at high speed from the exhaust of the rocket. The exhausted fuel now has some linear momentum in our reference frame. The total linear momentum before the firing of the engines was zero. Since it is conserved, the total must remain zero. This means that the momentum of the fuel in the backward direction must be exactly balanced by the momentum of the rocket in the forward direction. Therefore the rocket moves forward.

Linear momentum is the product of mass times velocity. If we know the mass and speed of the exhausting fuel at any instant, knowing that the product of those numbers must equal the mass of the rocket plus its remaining fuel, times the rocket's speed you could calculate the speed of the rocket without knowing anything about the forces involved, just from the conservation of linear momentum. Of course we could calculate the force experienced by the rocket once we know how its speed changes over time by applying Newton's second law that force equals mass times acceleration.

These ideas are easy to express in words as I have done here, but the mathematics in the case of real rockets gets very messy. You can probably find some examples in your text book, set up to be easily solved.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ