Example

Dress Rehearsal

You have studied Isaac Newton’s work on the laws of motion. You are now reading and learning about Newton’s third law of motion, action and reaction. You will be examining the relationship between these two terms. You’re curious about this since it’s all about force. Your teacher tells you that when you’re walking on a sidewalk, the sidewalk pushes against your foot just as much as your foot pushes against the sidewalk. Honestly? You just can’t see it.

Here’s how the text analyzes action and reaction: Force is defined as a push or pull, but force is really defined as an interaction between two things, such as your foot and the sidewalk. Here is Newton’s third law: “Whenever one object exerts a force on a second object, the second object exerts and equal and opposite force on the first object.” One of these is called an action force, the other a reaction force. It doesn’t matter if the foot or sidewalk is called the action force since the forces are EQUAL. This relationship exists in pairs. One does not exist without the other.

Hence, Newton’s third law is: To every action there is always an equal opposing reaction. 

What about friction? In the case of your foot and the sidewalk, you swimming in the water, or car tires hitting the road, actions and reactions take place. How does your foot, your body, and car move forward rather than remain in place? Well, friction must be present in order for a reaction to take place with a consequent forward motion.

Now, one must also consider the mass of the objects as they act and react together as Newton described in his second law. In the second law, Newton stated that acceleration of an object is not only proportional to the net force, it is inversely proportional to the mass. See how you can’t just learn about one concept in isolation? All these scientific concepts are connected, so you have to understand them each individually AND how they are related. Hey, we didn’t say it would be easy.

Consider a bullet fired from a rifle. The bullet speeds forward while the rifle retracts. Newton’s rule says that the smaller the mass, the greater the acceleration. The greater the mass, the smaller acceleration. So, in this example, the bullet and the rifle interact. The force between the two is equal and in opposition. After the shot is fired, the bullet accelerates faster than the rifle retracts because the mass of the bullet is smaller than that of the rifle. NOW, you get it!

This fulfills Newton’s law. It’s why rockets shoot, and birds and airplanes fly. All made possible by the law of action and reaction.

Source:

Hewitt, Paul G. Conceptual Physic, 3^rd edition. California: Addison-Wesley Publishing Company, 1997.

Drill

Using the following explanation about Newton’s theory of gravity, determine the key terms, consider the relationships among them, and describe those relationships in written form.

Newton's Gravity

In the 1600s, an English physicist and mathematician named Isaac Newton was sitting under an apple tree, or so the legend tells us. Apparently, an apple fell on his head, and he started wondering why the apple was attracted to the ground in the first place.

Newton publicized his Theory of Universal Gravitation in the 1680s. It basically set forth the idea that gravity is a predictable force that acts on all matter in the universe and is a function of both mass and distance. The theory states that each particle of matter attracts every other particle (for instance, the particles of "Earth" and the particles of "you") with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

So the farther apart the particles are, and/or the less massive the particles, the less the gravitational force.

The standard formula for the law of gravitation goes [source: UT]:

Gravitational force = (G * m1 * m2) / (d²)

where G is the gravitational constant, m1 and m2 are the masses of the two objects for which you are calculating the force, and d is the distance between the centers of gravity of the two masses.

G has the value of 6.67 x 10E-8 dyne * cm2/gm2. So if you put two 1-gram objects 1 centimeter apart from one another, they will attract each other with the force of 6.67 x 10E-8 dyne. A dyne is equal to about 0.001 gram weight, meaning that if you have a dyne of force available, it can lift 0.001 grams in Earth's gravitational field. So 6.67 x 10E-8 dyne is a miniscule force.

When you deal with massive bodies like the Earth, however, which has a mass of 6E+24, it adds up to a rather powerful gravitational force. That's why you're not floating around in space right now.

The force of gravity acting on an object is also that object's weight. When you step on a scale, the scale reads how much gravity is acting on your body. The formula to determine weight is [source: Kurtus]:

weight = m * g

where m is an object's mass, and g is the acceleration due to gravity. Acceleration due to gravity on Earth, is 9.8 m/s², and it never changes, regardless of an object's mass. That's why if you were to drop a pebble, a book and a couch off a roof, they'd hit the ground at the same time.

For hundreds of years, Newton's theory of gravity pretty much stood alone in the scientific community. That changed in the early 1900s.

Source:
An excerpt taken from Layton, Julia.  "How does gravity work?"  01 April 2000.  HowStuffWorks.com.  http://science.howstuffworks.com/environmental/earth/geophysics/question232.htm  23 April 2012. Web.

ANSWER:

Key terms:

gravity, force, particle, matter, mass, proportional, dyne, acceleration.

Explaining the relationships between the terms:

Newton’s Law of Gravity states that gravity is a force between objects determined by the mass and distance of the objects. Each particle of matter attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This concept can be written with this formula:

Gravitational force = (.67 x 10E-8 dyne cm2/gm2 times the mass of object one times the mass of object two) divided by the (distance squared).

So, the farther away and the less massive the objects are, the smaller the resulting force, or gravity. Objects with greater mass, such as the earth, exert more force.

The force of gravity is also the weight of an object. A dropped object always falls at the same rate as any other object since the acceleration due to gravity (g=9.8 m/s² ) never changes.