Class content > Newton's Laws > Newton's Laws as Foothold Principles

Prerequisites

• Newton's 0th law 
• Inertia
• Interactions

In formulating our observations and understanding of how objects move, we need to coordinate our variety of experiences and intuitions together with what we have learned from our experiments into coordinating principles. We want these principles to be general -- to hold for all circumstances as long as we have carefully defined them. In Newton's 0th law, we have identified that what we have to do first is identify objects and interactions. For this, tools such as System Schema and Free-Body Diagrams help.

Once we have decided what objects and interactions we have, we need a starting point: What happens to an object (or system of objects) when all the interactions on it balance? (Or, one might consider what happens to an object if there are no interactions acting on it. This would only be a thought experiment since on the earth there are always interactions, starting with gravity.) The first intuition we might typically have is that if you want to get something moving and keep it moving, you have to push it. If we want to move a piano across a floor, we have to push in order to start it and continue to push in order to keep it going. When you stop pushing, it quickly comes to a stop.

A second example is just your own motion when you walk. When you stop pushing on the ground in order to walk, you just stop.

But these intuitions are a bit tricky. When we are pushing a piano, we are not the only object interacting with it. It also interacts with the earth via gravity and the floor via normal and frictional forces -- and these forces are as large or larger than the forces we exert. When we stop pushing, those other forces do not go away, so they have to be considered in deciding what it is that is happening to the piano. The same is true when you walk.

More than that, we have intuition in other circumstances that seem to contradict what we naturally feel about the motion of the piano. 

Consider that you are playing baseball and catching the pitches of a pitcher throwing a ball with a mass of about 150 grams at 40 meters/second (90 miles/hour). Here your intuition is (or should be!) that you do not want to catch this ball with your bare hands. It is not stopping just because no one is pushing it any more! It wants to keep moving and you will have to have a strong (and potentially painful) interaction with it in order to get it to stop. As a second example, think about the motion of a high speed train (Shikansen shown below).

If you knew a high speed train was coming through a railroad crossing, you would not (should not!) park your car across the tracks because "there is a long straight track and the engineer will see you and therefore stop the train"! It takes a lot of effort to stop a moving train -- and lots of interactions between the wheels and the track to slow it down and bring it to a halt. 

To make sense of both of these sets of intuitions together in order to decide how to think about motions with balanced forces, let's focus on the piano and the train. The piano stops almost right away but the train needs a lot of effort to stop -- possibly with a lot of squealing of brakes and perhaps even sparks coming from between the wheels and the rails. It's clear in the case of a stopping train that the interaction with the rail is critical. We can see that when we are pushing a piano -- or walking -- that the interaction with the ground is playing a role in making us stop. If you walk on ice and stop walking you don't stop, you slide. (Roll down to the bottom of this page to see a video of a goat sliding on a patch of ice. We don't put it in line with the text because it's too distracting!)

Thinking of trying to walk -- or stop -- on perfectly smooth ice gives us a good starting point. If we consider that ice reduces the horizontal interaction (force) with the goat on it (the vertical forces are balanced), we get an idea for a common principle:

Newton's 1st law: When all the interactions between an object and all other objects interacting with it are balanced, the object will maintain a constant velocity (which could be 0). 

This allows us to maintain both our intuitions:

• When an object is stopped, it needs an unbalanced interaction to start it moving.
• When an object is moving, it needs an unbalanced interaction to slow it down and bring it to a stop.

We might also add to this:

• When an object seems to slow down and stop for no reason at all, we should look for an interaction (force) that we have not considered.

This helps us to resolve our conflicting intuitions about pushing something along the ground. If we want to get it started, we have to unbalance the horizontal forces on it to overcome the resistance of the interaction with the floor to motion. When we are pushing the object at a constant speed, we are then balancing the resistive interaction from the floor so that the "moving on ice" situation is effectively restored. If there is no horizontal interaction (force) the object keeps moving at a constant speed, just like on ice. So when we push something at a constant speed we are cancelling the resistive force of the ground, not overcoming it. (We do need to overcome it to get the object started.)

This is a useful starting point for the study of motion that is consistent -- at least qualitatively -- with both of our intuitions. Our next step is to try to make our results quantitative. How much of a force will produce how much of a change in the velocity? This is the subject of Newton's 2^nd law.

Follow ons:

• System Schema 
• Free-body diagrams 
• Newton 1: Example 

Joe Redish 9/21/14