Newton’s Laws NotesLevel 1: Newton’s 1st LawWhat is a Force? How do we measure force?A force is a push or a pull. The unit for force is kgm

s2. It gets annoying to write kgm

s2

over and over, so we came up with a shorter name for this whole mess, called a Newton.

Newton= kgms2

The symbol for a Newton is N. If we were going to push a book across a table, for example, we might say that we pushed the book forward with a force of 15 N.

Forces as VectorsForce is a vector, so we care about its magnitude (amount) and we care about its direction. This also means that we can show forces by drawing them with arrows, just like we did in the past couple units. The greater the force, the longer the arrow. The arrow starts at the center of the object and points in the direction the force is acting. We will learn how to draw pictures like the one on the right in the next unit.

Newton’s LawsSee this guy? He was born premature on Christmas Day, just after his own father had died. His mother remarried and sent him away, something he never really got over. He was a stutter who loved to write lists. When he went home for a break during college, he invented calculus. Then he revolutionized the world by inventing mechanical physics. He was so driven by curiosity that he once voluntarily inserted a needle into his eye so that he could explore how sight worked. His name was Isaac Newton and many people consider him the greatest genius the world

has ever seen.One of the things Sir Newton was most famous for was his three laws of motion, often referred to as Newton’s Laws. These three laws help us predict and explain motion. In this unit, we are going to learn about all three.

Newton’s 1st LawNewton’s 1st Law states that an object in motion will stay in motion unless acted upon by an unbalanced force. An object at rest will stay at rest unless acted upon by an unbalanced force. Let’s take this apart piece by piece.

First, imagine you are in a space suit, floating in a starless universe. You are alone in the darkness, except for a football you are holding in your hand. You reel back and throw the ball. It flies away from you going 7.2 m/s. Newton’s 1st Law tells us that in this empty universe the football will continue to move forward at exactly 7.2 m/s forever (if we ignore its attraction to you, which we will get into later). Similarly, if we were to just put the football in one spot in space and leave it there, it would stay there forever.

Why don’t we see this happen on earth? When we kick a soccer ball here, it doesn’t go forever. It rolls along the grass, slowing down to a stop Why? Because in this situation, you have an unbalanced force acting on the ball. The grass is brushing against the outside of the ball, stealing energy from the ball, slowing it down. What about a plane flying through the air? It’s not even touching the ground. Why doesn’t it keep moving forward at the same speed? Because the air around it is brushing it, stealing its energy, trying to slow it down.

What if we had two people pushing against a box (see the picture)? They push and push and push but the box doesn’t go anywhere. Why is this happening? We have outside forces acting on the box- why doesn’t it start moving?

Here the key idea- an object will only start moving if the forces acting on it are unbalanced. In the situation above, the two people are pushing the exact same amount. This means they cancel each other out, and the box stays at rest.Key Idea: If two forces acting on an object are equal and opposite, they are balanced forces. They cancel one another out. If you have an object moving at a constant velocity, does that mean there are no outside forces acting on it? No. It just means the forces acting on it are balanced (they cancel out). Picture a plane at cruising speed, moving along at a nice constant velocity. The engines are pushing it forward with the exact same force as the air resistance is pushing it back. The two forces are balanced, so they cancel out and the plane keeps moving forward at a perfectly constant speed.The chart below summarizes this idea.

Figure 1: From http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law

Objects that have balanced forces acting on them will keep doing what they have been doing. If they have been at rest, they will stay at rest. If they were in motion, they stay in motion. If an object has an unbalanced force acting on it, it will accelerate. This means it could be slowing down, speeding up or changing direction. We will look at this more carefully in the next section. We call an object’s desire to keep doing what it has been doing inertia. Objects with more mass have more inertia. For example, a train which is in motion is a lot harder to stop that a Prius that is in motion. The train has more mass, so it has more inertia. This means that if it is moving, it want so keep moving.

Level 2: Newton’s 2nd LawWhat is mass?The mass of an object is how much stuff the object is physically made of. That won’t change no matter where we take it in the universe (unless it is ripped up, or cuts its hair or poops or something). This can be tricky for physics students because we don’t really have a word in typical day to day English that means “mass”. We almost always talk about weight. It can be a hard concept to understand. We measure mass in kilograms, which is a unit of measurement used pretty much everywhere in the world except the US. One kilogram is approximately the mass of a large water bottle full of water.

Newton’s 2nd LawNewton’s 2nd Law is hard to explain in words. It’s actually easier to understand in equation form. Here it is:

Fnet=ma

Let’s look at this piece by piece. m stands for mass, which is measured in kg. a stands for acceleration, which is measured in m/s/s or m/s2

Figure 2: About 1 Kilogram

Fnet stands for “net force” or total force. In other words, if we were add all the forces up on an object, this would be the total amount. Example Problem

The box above has one force acting on it (gravity) which pulls it with a force of 600N. If the box has a mass of 61.2 kg, what is the acceleration of this box?SolutionWe know the mass is 61.2 kg because the problem gave that to us. m=61.2 kgBecause there is only one force acting on the box, we can say:Fnet=600N

Write the equation:Fnet=ma

Plug n’chug600=(61.2)a

60061.2

=a

a=9.8 ms2

F net (F net) is called a lot of different things: the net force, the total force, or the resultant force. They all pretty much mean the same thing- add the forces acting on the object together. Sometimes people show this with a little summation sign, too.

Fnet=∑ F

Don’t let that symbol scare you. It just means that you need to add up all the forces acting on the object. It basically means Fnet. This is actually used pretty widely in higher level math. It just means “add up”. For example, let’s say you were given three paychecks this month- one for $100, one for $150, and another for $100. We could say:

∑ paychecks=100+150+100=$350

The example above focused on adding money. What if we wanted to add forces, which are vectors. We follow the same rules we did with other vectors. You need to take direction into account.

Rules for adding forces:1. Forces that act in opposite directions subtract from one another.

Example2 N 10

Net force: 8 N2. Forces that act in the same direction add to one another.

Example

Net force: 12 N3. Forces acting at right angles can be found using the Pythagorean

Theorem.Example

Net force: 10.77NObjects that have unbalanced forces acting on are accelerating.

Practice ProblemFor each of the situations below, find the net force acting on the box.

The Solution

It can be hard to keep track of what happens to objects in different situations. The chart below summarizes what we’ve learned so far.

2 N

10

4N

10

4N

10

10.77 N

Level 3: Mass and WeightBefore moving on to the last of Newton’s Laws, let’s talk about the difference between mass and weight.

The mass of an object is how much stuff the object is physically made of. That won’t change no matter where we take it in the universe (unless it is ripped up, or cuts its hair or something). This can be tricky for physics students because we don’t really have a word in typical day to day English that means “mass”. We almost always talk about weight. It can be a hard concept to understand. Weight is a type of force that tells us how much we are being pulled toward the ground we are standing on.Weight = Force of gravity We often see it written as Fg, though sometimes people just write W. In physics, we do not typically measure weight in pounds- we state it in Newtons. The equation for weight is:

Fg=mg

Where Fg is the force of gravity (weight), m is the mass, and g is the acceleration due to gravity. On earth, the acceleration due to gravity is -9.8 m/s2.The weight, however, is dependent on the acceleration due to gravity at its current location. This can change if you go to a different planet with a different acceleration due to gravity.

The other thing to keep in mind is that weight is a force that pulls the object down. In physics, we often say that up is positive and down is negative. Because of this, you will often see weight negative.Practice ProblemThis puppy has a mass of 4 kg. What is the puppy’s weight?Solution

Fg=mgFg=(4 )(9.8)

Fg=39.2N down

Level 4: Newton’s 3rd LawThe Law:For every force, there is an equal and opposite force.

How to think about this:For every force, there is an equal and opposite force. If, for example,

a bat hits a ball, the ball exerts the exact same amount of force back on the bat. This doesn’t mean they experience that

force the same way. The ball has a smaller mass, so it experiences a much greater acceleration. Here’s another example. Imagine that an elephant on roller skates. You are standing in front of the elephant, also wearing roller skates. You push off the elephant with a force of 30 N. The elephant would feel the exact same force- 30 N- but in the opposite direction. You both experienced equal and opposite forces. This doesn’t mean it feels the same to both of you. The elephant has a HUGE mass, so he will have a very small acceleration. You have a much smaller mass, so you would have a pretty large acceleration.

Here’s one that really messes with people’s heads. The earth is pulling you down toward its surface with a force of about 600 N, depending on your mass. How much are you pulling up on the earth? That’s right 600 N. Why then, when you jump, does the earth not rise to up and meet you? Because the earth’s mass is astronomically larger than your mass, its acceleration is so tiny it is undetectable.