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Newton’s Laws and Making a Rocket Go

In about 1687, Isaac Newton came up with three laws:

  1. An object at rest tends to stay at rest and an object in motion tends to stay in motion unless an external force acts upon it.
  2. A force applied to an object is equivalent to its change in momentum. Most people think of this as being the formula F=ma, where F is the force (a vector, hence it is in bold, meaning that it has both magnitude and a direction, like up or down), m is the object’s mass (a scalar), and a is the object’s acceleration (another vector). Keep in mind that this is a simplification, though! Really, force is a change in momentum, which is the product of the object’s mass times its velocity. This will be discussed below.
  3. For every action, there is an equal and opposite reaction.

The first law is describing something like cars accelerating and decelerating (for example). The second law is sort of a quantification of this – how much force you have to apply to make something accelerate and decelerate. Well, it is mass related. If the object is very big (a aircraft carrier, for example) it takes a LOT of force to accelerate it. If the object is small (a rabbit, for example) it can be accelerated very, very quickly. Newton’s third law is the law that is going to help us get into orbit. The classic example of this law in action is two skaters standing on ice. If they are about the same size, and they push off of each other, they both go backwards with about the same speed.

 

ice_skaters_equal
If two ice skaters who are the same size push off of each other, they will both move backwards with the same velocity. This is because they have the same mass, so both their velocity and momentum are equal.

If you combine the second and third laws, you can envision what would happen if you had a very big skater and a very small skater push off each other – the big skater would not go backwards very fast, while the small skater would move backwards very fast. This is the heart and soul of rocketry!

If the ice skaters are different size from each other, and they push off of each other, their momentum must be equal to each other, so that means that the big person will move much slower than the small person.
If the ice skaters are different size from each other, and they push off of each other, their momentum must be equal to each other, so that means that the big person will move much slower than the small person.

It is sometimes hard to understand the last law in the world we live in. For example, if you push off of a brick wall, the wall doesn’t move backwards. If you push off the ground, the ground doesn’t move. This is really because the brick wall and the world are either too massive for a tiny force to really matter, or the force that you apply are absorbed in a way that you don’t really see. But, take it from me – the forces are really there and they really work. For example, take a very large car and put it on a very flat road in neutral with the parking break off. If you push on it, it will move. Very slowly, but it will move. If you put the parking break on, it won’t move. This is because you don’t have enough strength to overcome the frictional force that is keeping the car in place (neither do I).

Let’s take the example above with the big skater and little skater and generalize it to something that every American can relate too: guns! (Actually, I don’t own a gun, unless you count nail guns, then I own 4 of them!) If you take a big football player and have them fire a tiny gun, then they wouldn’t move backwards hardly at all, but the bullet would move out quite quickly.

If a big person fires a tiny gun, then the kick back is not very much. This is because the momentum of the bullet is small, which means that the football player's momentum would also be small, and since their mass is so large, the backwards velocity would be tiny.
If a big person fires a tiny gun, then the kick back is not very much. This is because the momentum of the bullet is small, which means that the football player’s momentum would also be small, and since their mass is so large, the backwards velocity would be tiny.

Thinking about Newton’s second law, that says that a force has something to do with mass, we can understand this: The bullet has a tiny mass, so it moves forward quickly, while the football player has a huge mass, so he hardly moves at all.

We can describe this in terms of momentum, which is the product of the mass of an object and it’s velocity.  The bullet has a large velocity and small mass, while the football player has a large mass and small velocity.  Newton’s third law basically is saying that when the bullet leaves the gun, it has a certain momentum, therefore, the football player has to have exactly the same momentum in the opposite direction.

This, in essence, describes how a rocket works. The gas coming out of a rocket’s engine has a very small mass (compared to the rocket), but it is moving incredibly fast.  The rocket itself is HUGE, so it moves very slowly (at first).

After a minute or so, the rocket has expelled so much fuel, that the mass has decreased significantly, so that the mass of the rocket and the mass of stuff that is coming out are closer to equal, like this example:

If a little kid fires a bazooka, the kickback would be incredible, since the bullet is big and moving fast, making the momentum quite large. The kid's momentum must be large also, and since their mass is small, the velocity must be quite large.
If a little kid fires a bazooka, the kickback would be incredible, since the bullet is big and moving fast, making the momentum quite large. The kid’s momentum must be large also, and since their mass is small, the velocity must be quite large.

In this case, the mass of the little girl is still much larger than the bazooka bullet, but the bullet is still moving very quickly, and therefore the girl moves backwards pretty quickly also.  The momentum of the girl and the momentum of the bullet have to be equal and opposite.

Next time, we will take a closer look at Newton’s Second Law and learn how to calculate thrust!

(Artwork done by Alan Ridley)

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