Science: An Elementary Teacher’s Guide/Objects in motion

You can see things in motion all around you: on a school's playground full of happy students, in cars driving along the streets, in raindrops falling to the ground. Children on swings, going down slides, jumping rope, or playing soccer are all opportunities to make observations about motion. Eventually, the soccer ball will stop rolling, the swing will slow down and come to a stop, and a child may trip and fall to the ground. We can see behavior in motion occurring, but what actually causes the behavior? Is the behavior of motion applied everywhere in the universe? The answer can be found in Newton’s three laws of motion, which he published in 1687.

Newton's Three Laws of Motion:

Isaac Newton (painting from 1689)

Sir Isaac Newton was one of the greatest scientists and mathematicians that ever lived. He was born in England on December 25, 1643. He was born the same year that Galileo died. He lived for 85 years. Isaac Newton was raised by his grandmother. He attended Free Grammar School and then went on to Trinity College Cambridge. Newton worked his way through college. While at college he became interested in math, physics, and astronomy. Newton received both a bachelor's and master's degree.

While Newton was in college he was writing his ideas in a journal. Newton had new ideas about motion, which he called his three laws of motion. He also had ideas about gravity, the diffraction of light, and forces. Newton's ideas were so good that Queen Anne knighted him in 1705. His accomplishments laid the foundations for modern science and revolutionized the world. Sir Isaac Newton died in 1727.

Newton's First Law

"Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it." Force is a push or pull that causes an object to move, stop, or change direction. In the absence of an unbalanced force, an object in motion will maintain this state of motion. This law is often called "the law of inertia" (inertia is the property of an object that resists movement by a force). This simply means that there is a natural tendency of objects to keep on doing what they're doing, to resist changes in their state of motion, whether that means a resistance to starting or a resistance to stopping. An object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

This law of motion is qualitative--it describes how things work without providing exact measurements or mathematical formulas. What are some everyday examples of Newton's First Law? How does this apply to wearing seat belts? How does it apply to a game of pool or air hockey? How does it apply to objects in outer space? What about the rotation of our own planet? What about sliding a heavy desk across the room?

If you roll a ball across the gym, it will eventually come to a stop. Is this in violation of the First Law of Motion? Pay attention to the wording "in the absence of an unbalanced force." What forces are acting on the ball? A nice demonstration would be to have a ball sitting in the middle of a wagon. What happens to the ball when you start pulling the wagon? Now that the wagon is rolling, what happens to the ball if you suddenly stop?

Newton's Second Law

Stated simply, the amount of Force needed to change an object's acceleration is dependent upon the mass of the object.

The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object). Everyone unconsciously knows the Second Law. Everyone knows that heavier objects require more force to move the same distance as lighter objects. How does the second law apply to lifting weights? To shooting a gun? What about a car accident?

The law is represented in the following basic form (the system of measurement is chosen such that constant of proportionality is 1):

${\vec {F}}={\frac {d(m{\vec {v}})}{dt}}$

The product of mass and velocity i.e. $m{\vec {v}}$ is called the momentum. The net force on a particle is, thus, equal to rate change of momentum of the particle with time. Generally mass of the object under consideration is constant and thus can be taken out of the derivative:

${\begin{aligned}{\vec {F}}&=m{\frac {d{\vec {v}}}{dt}}\\{\vec {F}}&=m{\vec {a}}\end{aligned}}$

The amount of force acting on an object is a product of its mass and acceleration:

${\vec {F}}=m{\vec {a}}$

alternatively, acceleration can be seen as the force acting on an object, divided by its mass

${\vec {a}}={\frac {\vec {F}}{m}}$

Examples:

• If you use the same amount of force to throw a soccer ball and a bowling ball, the soccer ball will experience faster acceleration than the bowling ball, because the soccer ball has less mass.
• If you drop a bowling ball and a soccer ball from a ladder, the acceleration due to gravity will be the same (they will travel at the same speed), but due to the increased mass, the bowling ball will hit with greater force.
• Imagine you and your friend are moving desks down a hallway and want to move at the same speed so you can talk. One of you is pushing a very heavy desk while the other is pushing a very light desk--the amount of force needed to move at a particular speed varies with the mass of the desk.

Newton's Third Law

For every action there is an equal and opposite reaction. This means that for every force there is a reaction force that is equal in size, but opposite in direction. That is to say that whenever an object pushes another object it gets pushed back in the opposite direction equally hard. If one object A exerts a force Fa on a second object B, then B simultaneously exerts force B on A.

Examples:

• When you jump off a small rowing boat into water, you will push yourself forward towards the water. The same force you used to push forward will make the boat move backwards.
• When you lean against the wall, it is pushing against you with the same force that you are pushing against it. This may be more apparent if you have one student lean against another student (the student acting as the wall will have to exert force to keep the other student from falling over).
• Ex. The baseball forces the bat to the left (an action); the bat forces the bat forces the bat to the right (the reaction).
• Ex. When air rushes out of a balloon, the opposite reaction is that the balloon flies up.

Outside Resources

• Professor Dave explains Newton's First Law, Second Law, and Third Law. These are highly recommended!
• Here is a Crash Course video on Newton's Laws of Motion
• Khan Academy lecture on First Law
• Veritasium exposes a common misunderstanding of the Third Law

• Rap-style music videos on Newton's Laws of Motion:
  • First Law
  • Second Law
  • Third Law

Quiz Yourself

Fill in the blanks

• First Law: An object at ___ tends to stay at ________, and an object in ________ tends to keep moving with the same _________ unless an ____________ force acts on it.
• Second Law: The amount of ________ needed to make an object change its ____________ depends on the _______ of the object.
• Third Law: When one object exerts a ________ on a second object, the second object exerts an __________ and __________ force back on the first object.

True or False?

• For a book sitting on the table, all forces acting on it are balanced.
• If an object is not accelerating or decelerating, no forces are acting on it
• An object's inertia causes it to come to a rest position.
• The only way to slow down a moving object is to apply a net force to it.
• Objects tend to stay moving because of a force called inertia.

Which Law?

• Which of Newton's Laws explains why satellites need very little fuel to stay in orbit?
• A frog jumps from a lily pad but instead of continuing in a straight line it is pulled down by gravity, landing in the water.
• After starting your car you notice that if you give it more gas by pushing on the accelerator, it goes faster.
• You are standing up on a bus and when the bus stops suddenly your body is thrown forwards
• Little 5-year old Juan is throwing rocks with his dad, but gets upset that the rocks he throws do not go as far as his dad's rocks.
• A swimmer pushes back on the water with her arm, but her body moves forwards.
• When I lean against the wall, I do not fall down.
• A person is in a car that has no head rest. When the car is hit from behind the person suffers a serious neck injury.

Define

• Inertia
• Force
• Acceleration
• Speed

Solve it!

• A car with a mass of 1,000 kg is at a stoplight. The light turns green, the driver pushes the gas pedal, and the engine applies a net force of 4,000 Newtons (a Newton is a unit of force). What is the car's acceleration?
• What is inertia?
• A billiard ball and a golf ball travel towards each other at the same speed. What happens when they collide?
• [BONUS] When you hit a baseball with a bat, the ball pushes on the bat with an equal but opposite force that the bat exerts on the ball (Third Law). Why is it that the ball changes direction and goes flying away, but that the bat continues moving the same direction it was going? What effect did the ball have on the bat? Can you use the Second Law to explain all the interactions between the bat and the ball? How does the First Law play into all this?