Up until now, the Phlying Physicists have been talking about how objects move, but we really didn’t concentrate on why they do. This study, (and you thought kinematics was hard) is called dynamics.

We have been talking a lot about acceleration and its relationships with distance, time and velocity. But the guy, the genius, who studied the causes of acceleration was Sir Isaac Newton. Contrary to the popular belief, Isaac was not responsible for creating the Fig Newton, but actually came up with three laws about forces and motion, which will be discussed in the next paragraph.

Before we jump right in and discuss these three laws Newton made about motion, we need to learn some physics terms. The thing which causes acceleration is a force. There it is, one of the biggest words of physics – force. A force can be simply defined as a push or pull. For example, when you are reading this page and have to scroll down, your fingers exert a force on the mouse key. Simple. So you can safely assume that there are literally trillions of different forces because we could be doing anything. But genius scientists such as Newton and Bill Nye the Science Guy (no wait . . . not Bill) have grouped forces into four groups, namely: Gravitational force, electromagnetic force, nuclear force, and weak force. (We will not be going into the depths of nuclear or weak forces). There is a picture of Isaac Newton below.

Now, to understand Newton’s first law, let’s play a game. Close your eyes and imagine a big green field with six people. Three people are wearing red, and three people are wearing blue. The reds are having a game of tug-o-war with the blues. If both teams pull with equal strength, the rope will not move. But, if the red team pulls with more strength, the rope will accelerate towards the red. The rope accelerated because there was an unbalanced, or a net, force. (Just to let you know, if we talk about a negative force, it doesn’t mean that there is not one there, just that it is directed in a direction opposite of a positive force. So, just to standardize, negative force means it is moving to the left, west, down, or south of 0, and positive means that it is moving right, east, up, or north or 0. This is for all vectors, not just force.) Newton’s first law dictates: an object with no net force acting on it will remain at rest or will remain in motion with constant velocity in a straight line. That is really deep. Take a minute to think about it until it becomes a part of your soul. Well, maybe not a part of your soul. As long as it remains in your brain, we won't get mad.

Newton had basically summed up why an object accelerates or stays at rest – because there is or isn’t a net force. But how much will an object accelerate when a force is exerted? Let play our game again. This time we are at a bowling alley. You see a 4 year old child with a fifteen pound bowling ball. How fast would the ball travel down the lane. (Just in case you don’t remember being a four year old, you can’t exert very much force, those muscles have not developed yet). A big mass with a small force is not going to get the ball accelerating very much. Then imagine this massive body builder (All physicists are huge bodybuilders, you know) who is trying to roll this tiny golf ball. He can really accelerate that thing. So, we can start to see a relationship. As the force gets bigger, you have more acceleration and as the mass gets bigger you have smaller acceleration. So, we can write it:

a = F / m

or more commonly written:

F = ma

This wonderful discovery is Newton’s second law of motion.

But wait, now we have another formula (OH NO!!) So, we need units to go along with it. We know the unit for acceleration is m/s/s and mass (oh, that is what the m is!?) is measured in kg, so the unit of force should be the kg-m/s/s! In honor of our physics father, the kilogram-meter per second per second will be called . . . the Newton (N).

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Example Problem

What is the net force required to accelerate a 1500kg race car at 3m/s/s?

Answer:

Well, how many formulas do we know for force? And we just learned one, so this shouldn’t be too difficult. Using F=ma, we can deduce that F=(1500)(3) = 4500N. Wow.

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Newton has another law. (This is getting to be too much, but the guy was a genius!) Let us go back to the bowling alley. If you were not feeling too well in the brain, and you wanted to kick you fifteen pound bowling ball without your shoes on, as hard as you possibly could, would you do it? Why not? Why would it hurt? If you kick the ball, you are exerting a force - and the ball should accelerate nicely away from you, into the crotch of your opponent. Uhh.. never mind that last bit.

When you exert a force on the bowling ball, the bowling ball exerts a force on to you too! Newton’s third law: When one object exerts a force on a second, the second object exerts a force on the first THAT IS EQUAL IN MAGNITUDE but opposite in direction. So, the harder you kick your bowling ball, the harder it will kick you back. Sort of. You get the idea though, right?

Remember acceleration could also be caused by gravity. Well, that is why we have weight, because gravity causes us to accelerate towards the earth. So, instead of using the formula F=ma, we can substitute, like we did before, ‘a’ for ‘g’, and then Force (F) becomes Weight (W): W=mg And always remember, g = -9.8m/s/s

If you push a large dirty crate on your mothers new Persian rug, two things will happen. First you will probably lose your life, but more importantly, the crate will stop as soon as you stop pushing. If you take away the rug, and push it on a polished wood floor, the crate will probably continue to move half a foot after you let go. It slides, because the floor is smooth. If you go outside, and push it on some ice on the street, the crate will go even farther. If you coat the bottom of the crate with ice as well, the crate will practically fly. Do you see where we are taking this? Friction is a force which opposes the motion between two surfaces that are in contact. If you have two smooth surfaces, you have less friction. The direction of the force of friction is parallel to the direction of movement.

	This is an aplet by IBM which demonstrates friction, motion and gravity. Click on the button that comes up.

We are now going to do some more work where the net force causes acceleration. Lets suppose a 10kg stone is resting on the ground. Assuming this is the smoothest stone, sitting on the smoothest ground, in the smoothest world in the smoothest universe (if you still don’t get it, pretend that there is no friction). A 100N force is exerted. The stone will accelerate 10m/s/s because a = F/m which equals 100 / 10 which is 10m/s/s.

Now, lets say instead of all of that smoothness, there is a force of friction of -20N. (Negative because the force is going in the opposite direction). Instead of using the 100N we were originally gave you, you have to find the net force. Only then can we use our famous F=ma equation. Now, since we have friction to take into account, our new formula is: Fnet = ma. With this equation you are asking how we find the net force.

Remember the field with the red and blue people, pulling eternally on a rope for our benefit? Let’s say the red was the friction and the blue was the applied force. If the blue exerted a force of 100N and the red exerted a force of 20N (it should be -20N when we put these numbers in our formula), the net force would be 80N. We can do that in our head. But, when the numbers get more complicated in class, here is the formula:

Net force = Applied Force + Friction Force

So, for our stone problem, the net force is equal to:

Net force = 100N + (-20N)
= 80N

Then, we can plug the net force back into the F = ma formula and see what the acceleration is, although the gifted ones among you reading this have probably already started up the calculator we provided and have done the calculation.

a = 80N / 10kg = 8m/s/s (You didn’t need a calculator for that!)

When you are using W = mg, the net weight is equal to the force of the ground plus the weight. For example, a 10kg stone just lying there will have a net force on it of zero because it weighs -98N (10kg x -9.8m/s/s) and the force of the ground underneath it is 98N (How do we know? Because the stone is not moving!). Therefore, the net force on the stone is 98N + -98N = 0N

Suppose Phred Physicist came along and threw the stone in the air. Now, the weight of the stone stays the same (-98N) but the force of the ground (or Phred) is lets say 148N. (Phred is not very strong) Then, the net force is 50N (148N + -98N). Then, we can add that into our formula:

a = F / m
a = 50N / 10kg
a = 5m/s/s Now, the stone has an acceleration.

Before you continue, you should make sure you know how to use vectors. The most common thing you will be doing with vectors is adding them, but it is not simple arithmetic.

You have already done a few problems with vectors. For example, add a pull of 3N, east and 2N, west- you have a net force of 1N, east. But, how did you do that? You probably did it algebraically. Since you can decide east is be positive and west is negative, you can then add 3 and -2, which gives you one. And since the answer is positive, the answer would be east. Tis method only gives you a possible 2directions, positive and negative. Vectors, however, can be anywhere—they could be travelling in any of the degrees of the circle: from 0 degrees to 360 degrees.

Here is an example vector problem: Two people kick a soccer ball. The first person kicks it north (90 degrees) with a force of 100N and the second person kicks it west (180 degrees) with a force of 212N. How much force was used, and in what direction?

You always start with your object at the point (0,0). First of all, you draw the first vector (100N, north) then, starting where you left off, draw the second one. You simply treat the end of the first vector as the point (0,0). The you draw your resultant vector from start to finish. You can usually use the Pythagorean theorem (you know, squaring the sides, adding them up, then taking the square root to find the hypotenuse) to solve for the magnitude of the resultant. You then need to find the angle that the resultant makes. If you are familiar with trigonometry (Elementary mathematics), you know to find the marked angle- you divide 212 by 100 and take the inverse tangent. If you don't know what a tangent is, don't worry about the angle for now.

If you have two balls, and they are both allowed to fall freely, and they are both dropped at the same time, but one ball is pushed horizontally as it falls, which ball will hit the ground first?

They both will hit the ground at the same time! If you look carefully at the picture below, you can tell that even though one ball is moving to the right with a constant velocity, both balls fall at the same rate downwards. The horizontal motion does not affect the vertical motion.

	This link opens up a new window which contains an interesting demosstration of the independance of horizontal and vertical motion.

Let’s think about this. The horizontal velocity has nothing to do with the vertical velocity. If you fire a bullet straight out into a field, and drop another bullet exactly at the same time, both bullets will hit the ground at the same time, but one bullet will be really, really, really far away.

If you were going hunting for a monkey (Do not go hunting for monkeys after reading this, this is a hypothetical physics learning experience), you might be faced with the following predicament: The monkey is hanging from a tree. You know from a supernatural source that when you shoot the gun, at the exact same time, the monkey is going to let go of the tree. Where should you aim your gun? Five meters below the poor innocent animal? 10 meters? Actually, you guessed it, you aim the gun directly at the monkey, because both the bullet and the monkey would have fallen towards earth at the same rate and the bullet would still have hit it. (We do not condone cruelty to animals on this page, nor do we want to see a monkey get shot.)