Newton's 2nd in a nutshell
13/02/08 21:39 Filed in: Physics
First, I am not really sure why Newton got to call
this HIS law. Second, its not really a law. What
happens if you don't obey this law? Would I go to
physics jail? Ok, now for the good stuff. I am going
to try to give a brief summary of Newton's 2nd law.
Newton's Second Law:
This says that the total force on an object changes its velocity. The greater the force, the more the change. The greater the mass of the object, the less the change. If velocity as defined as the vector indicating the speed and direction the object is moving, then acceleration is the following vector:
If you are having difficulties with vectors, here is my short tutorial on vectors.
So, then Newton's Second Law can be written as:
Please forgive (and forget) all
the times you have seen this written as
"F=ma". This version is missing two
important aspects. First, it is not a vector
equation. Both force AND acceleration are
vectors. Second, it is the TOTAL (or net) force
acting on an object that is related to the
acceleration.
Alternative Concepts
This law (I will refer to it as N2) says that forces CHANGE the motion of an object. This does not agree with many common sense ideas
about force. If you look around you (and everyone does) you say that forces CAUSE motion. Its ok if you think this, everyone usually does. Aristotle was a pretty smart guy, and this is what he would say. Ask yourself this question:
Suppose you roll a bowling ball. What keeps it moving after you let go of it?
If you say, the force of the hand or the force of motion or something weird like that, you are like Aristotle.
If you say nothing keeps it moving - you are correct. Nothing keeps it moving because forces causes CHANGES in motion. If the bowling ball is moving at a constant speed, no forces are needed.
I see these "weird" forces all the time. Forces like:
Long Range:
These are forces that can be exerted by another object without having to touch that object. In introductory physics, you will likely on encounter:
These are forces exerted by objects that touch. Here are few examples:
Test Yourself.
Are you still not sure what you think about Newton's 2nd law? Here is an excellent little game to play from the University of Colorado:
To play this game, first click the "A" button to turn it into acceleration mode. Now, when you drag on the blue dot where it says "acceleration" it will give the red dot above that acceleration (in the direction and magnitude you choose). N2 says that the acceleration is the same direction as the force, so you can think of this as specifying the force. Now make the red ball move to the blue finish dot without hitting the wall. Aristotle would not do to well at this game.
Why does Newton's second law work?
This is a great question someone asked me the other day. I think people ask questions like this because they don't really understand the nature of science. How was this relationship created? Was it derived from something? The answer is that this is an experimentally determined relationship. It works because of no reason. Does this mean that it is wrong? Not really, it just means that it is a mathematical model that agrees with experimental evidence and allows us to make predictions. That is the essence of science.
This says that the total force on an object changes its velocity. The greater the force, the more the change. The greater the mass of the object, the less the change. If velocity as defined as the vector indicating the speed and direction the object is moving, then acceleration is the following vector:
If you are having difficulties with vectors, here is my short tutorial on vectors.
So, then Newton's Second Law can be written as:
Please forgive (and forget) all
the times you have seen this written as
"F=ma". This version is missing two
important aspects. First, it is not a vector
equation. Both force AND acceleration are
vectors. Second, it is the TOTAL (or net) force
acting on an object that is related to the
acceleration.
Alternative Concepts
This law (I will refer to it as N2) says that forces CHANGE the motion of an object. This does not agree with many common sense ideas
about force. If you look around you (and everyone does) you say that forces CAUSE motion. Its ok if you think this, everyone usually does. Aristotle was a pretty smart guy, and this is what he would say. Ask yourself this question:
Suppose you roll a bowling ball. What keeps it moving after you let go of it?
If you say, the force of the hand or the force of motion or something weird like that, you are like Aristotle.
If you say nothing keeps it moving - you are correct. Nothing keeps it moving because forces causes CHANGES in motion. If the bowling ball is moving at a constant speed, no forces are needed.
I see these "weird" forces all the time. Forces like:
- Force of the hand
- Force of the push
- force of the kick
- force of the speed
- force of the motion
- use the force Luke
Long Range:
These are forces that can be exerted by another object without having to touch that object. In introductory physics, you will likely on encounter:
- Gravitational force (force between objects with mass)
- Electrical force (force between object with electrical charge)
- Maybe you will see a magnetic force (force between moving electrical charges)
These are forces exerted by objects that touch. Here are few examples:
- Friction
- Normal force (between touching surfaces)
- Air resistance
- Tension (from say a rope)
- A hand (touching of course)
Test Yourself.
Are you still not sure what you think about Newton's 2nd law? Here is an excellent little game to play from the University of Colorado:
To play this game, first click the "A" button to turn it into acceleration mode. Now, when you drag on the blue dot where it says "acceleration" it will give the red dot above that acceleration (in the direction and magnitude you choose). N2 says that the acceleration is the same direction as the force, so you can think of this as specifying the force. Now make the red ball move to the blue finish dot without hitting the wall. Aristotle would not do to well at this game.
Why does Newton's second law work?
This is a great question someone asked me the other day. I think people ask questions like this because they don't really understand the nature of science. How was this relationship created? Was it derived from something? The answer is that this is an experimentally determined relationship. It works because of no reason. Does this mean that it is wrong? Not really, it just means that it is a mathematical model that agrees with experimental evidence and allows us to make predictions. That is the essence of science.
