An Introduction to Newton's Laws, Momentum, and Energy

An Essay By Hannah D. // 6/29/2017

My latest science lesson for the homeschoolers at my local library! Launching marshmallows into their mouths was a highlight. I sent them home with their own catapults and a sugar high.

Materials
Popsicle Sticks - regular and jumbo
Marshmallows
Skinny rubber bands

Plastic Rain Gutters
Easter Eggs
Marbles
You can use a protractor if you want the exact angles listed in the table for this exercise, but really all you need is a general estimate of slight, medium, and steep angles (if you have some math-minded students, showing them how to use a protractor could have it's own benefits, though)

A ruler with a groove in it (or a grooved surface - explained under "Energy" secion)

Hotwheels cars
Some other, larger-sized, Hotwheels-like toy car that has more mass than the Hotwheels and can collide with them (i.e. they won't just roll underneath the larger car, but actually bounce off of it)

Newton’s Laws

  1. Inertia: An Object in Motion Stays in Motion, and an Object at Rest Stays at Rest (unless something else stops it)
  2. Force is equal to mass times acceleration.
  3. For every action, there is an equal and opposite reaction.

Newton’s First Law: Inertia

Slide a box, some cars along the table. Why does it stop sliding if inertia is true? Friction is a force that stops it. Now try a marble. Marbles take a lot longer to stop because of their spherical shape. They’re only ever touching the table at one tiny little point, so there isn’t much friction there. If you’re ice skating, it takes a lot longer to stop because the friction from ice is weaker than the friction from the ground.

Newton’s Second Law: F = ma

 Mass and weight are two different things! You’re mass is how much “stuff” you are; your weight is actually a force from earth’s gravity pulling on your mass. If we were on the moon, we would all have the same mass, but the moon is much smaller than the earth, so its gravity is weaker. That means we would all weigh less on the moon! That’s why astronauts can jump and float around on the moon. Jupiter, however, is much larger than earth. If we were on Jupiter, we would weigh so much, it would be nearly impossible to even walk up the stairs.

Acceleration is how fast something changes speed. Your speed, or velocity, is how fast you are moving. Acceleration is the change in your velocity – as you speed up or as you slow down. When you drop something (like a marble), it falls under the acceleration of earth’s gravity. We can also play with different accelerations down this ramp.

We can set up the ramp at different angles – steep or mild slant – and we can put different masses in the box to slide down it. We can’t measure acceleration, but we can measure the amount of time it takes for the box to hit the floor. The less time, the faster the acceleration. The more time, the slower the acceleration.

Let's use a table for recording our observations, in this case, the time it takes for each of our trial runs.

Time for Boxes to Slide to Floor

 

 

 

Mass #1

 

Mass #2

 

Mass #3

 

       15˚ Incline

 

 

 

 

       45˚ Incline

 

 

 

 

       75˚ Incline

 

 

 

After filling in the numbers from our experiment, we can conclude some things from the data. The mass doesn’t change the acceleration in this case. However, increasing the angle does change the value of the acceleration! When you take physics in high school, you will learn the math behind objects sliding down inclined ramps. And you will discover that the masses of the objects cancel out of the equation for acceleration! That means that for objects sliding down inclined planes, mass doesn’t affect acceleration at all.

Galileo Galilei experimented on this five hundred years ago when he dropped light and heavy things off of the Leaning Tower of Pisa. Now, if I drop a feather or piece of paper with a marble, the marble does hit the ground first. That's just because of air resistance, however. Galileo predicted that if you dropped a heavy object (like a marble) and a feather at the same time in a place with no air, they'd hit the ground at the same time. Five hundred years later, Neil Armstrong and Buzz Aldrin landed on the moon - where there is no air - and conducted the experiment that was impossible for Galileo to conduct. Guess what? He was right! The feather and the massive object hit the moon's surface at exactly the same time!

Newton’s Third Law: Action and Reaction

For every action there is an equal and opposite reaction. When I push against the table, I am exerting a force on it. Newton’s Third Law says that the table is also exerting a force back on me! We know that that's true since if the wall did not push back at me, I'd go right through the wall! We can look at Newton’s Third Law more closely by applying to another physics topic: momentum. 

Momentum

What is momentum? From a mathematics perspective, we can say that:

momentum = mass x velocity

 Now, we know that mass has to do with the stuff inside of an object. And we know that velocity is just speed, how fast an object is moving. But what is momentum?

Perhaps we can get an intuitive feel of momentum by combining it with Newton’s Third Law. Let’s consider two cars driving towards each other. Something goes wrong, and they crash. That crash is an action. What is the reaction?

The cars move away from each other. Just how they move away from each other, however, is determined by momentum.

When we crash two cars that have roughly the same mass, how fast do they move away from each other? They both move away at around the same velocity. When you crash a big car with a little car, which car do you think will move away faster? That's right - the little car goes zooming away but the big car hardly moves at all. That’s because their momentums have to balance.

The big car has a big mass, so it gets a tiny velocity. The little car as a little mass, so it gets a big velocity. In that way, momentum is conserved (an important rule for the physics of crashes) and they both get the same momentum.

Big Car Mass: 10 grams                                  Big Car Velocity: 1 m/s
Little Car Mass: 1 gram                                   Little Car Velocity: 10 m/s

Big Car Momentum: (10 grams)x(1 m/s) = 10 “momentums”
Little Car Momentum: (1 gram)x(10 m/s) = 10 “momentums”

Energy

When studying motion, we can study the forces involved in motion, or we can study the energy involved in motion. We’ve already looked at forces by looking at Newton’s Laws. Now, let’s look at energy.

We’ll be considering two types of energy: what we call Kinetic Energy, and what we call Potential Energy.

Potential Energy considers how much energy is “stored up” in an object. The key image here is a priceless glass vase sitting right on the edge of the counter-top. If it budges even a little bit, the vase will fall and shatter! Before that happens, however, we say that the vase has potential energy – it has the potential to start moving.

Once the vase starts falling, however, it is moving. The energy of an object in motion is called kinetic energy.

We don’t have a priceless glass vase to demolish today, but we do have these marbles and other objects to drop. When I hold my marble in the air, it has potential energy. It’s not moving, but it could move. As soon as I drop the marble, it starts moving downwards, meaning the potential energy in my marble has converted to kinetic energy.  

Let’s take out our marbles and set them up in a straight line. Marble #1 should be all by itself, while Marble #2 and Marble #3 should be touching each other. It helps if these two are on a "race track" of sorts - perhaps the grout in between floor tiles, or the groove in some wooden rulers. That way, you prevent marbles from striking each other at angles (which causes a much more complex and erratic behavior in the collisions!)

Push Marble #1 so that it hits Marble #2.

How does Marble #2 respond?
How does Marble #3 respond?

When you push Marble #1, you give it kinetic energy, and it rolls towards the other two. The energy transfers through Marble #2 as potential energy and then transfers to Marble #3 as kinetic energy. That is why Marble #2 hardly moved and Marble #3 moved a lot! You can experiment further by lining up even more marbles in a row. If you slide one marble towards the line-up, only the one marble on the end will move. If you slide two marbles together towards the line-up, the last two marbles on the end will move! You can also see this sort of thing in a Newton’s Cradle, or if you have ever played with billiard balls.  

We can also watch potential energy convert to kinetic energy by playing with catapults. We have some catapults here to launch marshmallows with. When you push the launcher down, the rubber band on the other end stretches out. This stretch gives the rubber band a lot of potential energy. Let the catapult go, and it gives its marshmallow kinetic energy by launching it into the air! 

Experiments
If you'd like more information on what actually goes into the experiments/demos, here are links to the projects:

Easter Eggs Down Ramps: http://littlebinsforlittlehands.com/plastic-easter-egg-races-exploring-r...

Marbles and Energy: https://www.pinterest.com/pin/79798224624773394

Popsicle Stick Catapults: http://littlebinsforlittlehands.com/popsicle-stick-catapult-kids-stem-ac... (scroll down for video with just popsicle sticks and rubber bands)