Lesson #4: Of Motion, Forces, and Fish

I decided to put this one in a new thread cuz it starts talking about other stuff other than gravity...

Apologies for this being a more physical science based lesson rather than something new. I'll post something else later...I have a cool methematical one...

[quote="Seth Lustig"]Speakin' of gravity, I'm reminded of that quiz question about throwing a ball in the air inside a moving train car...essentially removing the wind-resistance or what ever. Now, if I'm not mistaken, the ball would fall mostly just straight down, technically moving forward with the train, even while not attached to it. Is that right? And given enough time, like if it fell really slowly, would it drift back toward the back of the train? Would fish in a tank? Why don't they?[/quote]

Let me first clarify the problem:

Q1:
You are standing in the middle of your room.
You throw a ball straight up in the air.
Where does the ball land?

A1:
The ball will land pretty much exactly where it started.

Note that small iperfections in the toss and air resistance, etc, might make the ball to move slightly off course and land slightly away from where it started, but it will still be pretty dang close.

Q2:
You are on a moving train.
You throw a ball straight up in the air.
Where does the ball land?

A2:
Same answer.

Most people would think once you let go of the ball, its floating inside the train and thus the train will move out from under it making the ball rocket to the back.

Q3:
If the rate of falling was MUCH much slower, where would the ball land?

Q4:
Since fish are suspended in a tank of fluid and the earth is spinning around beneath them, shouldn't they rocket into the side of the tank?

First thing we need to know is Newton's 3 Laws:
Law #1.
An object at rest tends to stay at rest.
An object in motion tends to stay in motion.

Law #2.
Acceleration is a function of mass and force.

Law #3.
Every action has an equal and opposite reaction.

We are most concerned with Law #1. I'm sure you've seen it before. But we can simplify it... "INERTIA"
(...Inertia is a property of matter...Bill Bill Bill Bill Bill...Bill Nye the Science Guy...)
Inertia is basically defined as an objects tendency to RESIST a CHANGE in motion. Meaning if its moving, it don't wanna stop. If its still, it don't wanna move.

The next thing we need to understand is what a force is. A force is simply a push or a pull.
Forces are also additive. Meaning if two people push the back of a stalled car, both of their forces will add together to make the pushing easier for both of them. However, when two forces are added that are going in totally different directions, the AMOUNT of the two forces stays separate.

For example, if one person was pushing the back of the aforementioned car to move it forward, I would not be helping at all if I was pushing on the side because the directions of the force do not cooincide.
But what does happen is the DIRECTIONS of the pushes add. Sounds wierd, but once again think of that car. You push forward, I push on the side, the car will go forward, but will also start turning in the direction of my push.

Now back to the ball question. What we need to recognize in this question is there are TWO forces working on the ball:

1) Your toss upwards.
Obviously you are exerting an upward force to cause the ball to fly upwards.

2) The train's motion.
The train is moving the ball FORWARD along the track. When you are sitting on the train, this doesn't seem to be happening because its sitting still in your hand. But if you were sitting in a car at a railroad crossing area, you would suddenly see that ball (on the train) go whizzing by.

These two forces are not added together because they are not going in the same direction. But their directions work together to make a rather interesting path of the ball. A parabola.

[img]http://www.physicsclassroom.com/Class/vectors/u3l2b1.gif[/img]

The two force directions add to make a sort of diagonal.

[img]http://www.physics.brocku.ca/courses/1p21_reedyk/images/W2-f03017b.gif[/img]

So to people on the outside of the train (not moving) it appears the ball is moving in a curved path (trajectory!).
To you on the train, it looks like its just going up then down.

So whats the point of me telling you ALL this stuff? Well again, the forces are interacting with each other, but they are not blending together...they are still very separate forces.

So what this means is if gravity was reduced or for some reason the speed of the falling object was reduced (perhaps creating more air resistence...like using a feather instead of a ball), only the speed at which it fell would change. Your force upwards would be the same. The trip down (from gravity) would just be a tad slower. The directions are still constant.

While it falls slower, it is STILL moving forward (with the train's motion) at the same rate.
So...

A3:
The ball (or feather or whatever) will still land in the same spot because the forward momentum of the train hasn't deviated.

If the train was to suddenly slam on the breaks as the ball (or feather) was in the air, the ball (or feather...do I need to keep writing that?), since it was not touching anything the ball would keep the same amount of foward momentum as it originally had. Thus the train would slow down underneath it and the ball would actualy land towards the front of the train.

The same thing would happen if you were in the back of a pickup truck and jumped up in the air, just as the driver slammed on the breaks.

Lastly...the fish.
The earth is spinning at a fairly good rate (like 900 mph). Why don't the fish go flying in the opposite direction to slam into the glass at 900 mph?

Water has alot more mass than most people think. Its actually kind of hard for something to move through it. There is alot of fluid friction there that pushes you back.
So a fluid like water in a container acts much like a single object. Including the fish.

So its kinda like you on the train. You don't continue to get pushed back into your seat because you eventually take on the same motion as the train. Its kinda like you become PART of the train. Just like the fish in the tank. Just like the fish on the 900 mph moving planet. Just like YOU on the planet.
We all are being pushed by the earth's movment...