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We will review the concepts of force, inertia, mass, weight, and the three laws of motion first developed by Sir Isaac Newton.
We previously covered concepts concerning the Earth sciences and our understanding of how the universe began. The Big Bang theory is the most likely explanation with scientific evidence for the genesis of our universe. It hinges on the idea that our universe expanded out of a tiny primeval fireball and that this expansion continues as galaxies today still move farther away from each other.
The foremost Italian scientist, Galileo, successfully eliminated the notion that a force was necessary to keep an object moving by introducing the notion of inertia. His observations paved the way for Newton to formalize the laws of motion, and he is often credited as the Father of physics.
To start us off let us review some terminology. In physics, a force is a push or pull. For example, a push or pull on an object would be considered to be a force. When one object pushes or pulls on another object, both objects exert an equal but opposite force on each other. Friction is the force caused by irregularities in the surfaces of the objects that are in contact and moving relative to one another. Any two objects, no matter how smooth they are, have some frictional force between them when they are moving relative to one another. If there was no such thing as friction, a moving object would need no force whatsoever to remain in motion. Objects in a vacuum theoretically move without friction.
When a rocket engine ignites on a launching pad, what can be determined about forces acting on the rocket ship?
The correct answer is B. In order for the rocket to lauch into space, it must overcome the gravitational force of the Earth acting on its mass. The burning rocket fuel expelled out the back of the rocket causes a forward thrust that is greater than the weight of the rocket and the air friction acting on it. Hence the rocket accelerates upward.
How can two objects with the same mass have different weights? The terms weight and mass are often used interchangeably and thus are often confused with each other. We think that a heavy object contains a lot of matter, but this is not always true. We often determine the amount of matter in an object by weighing it on a scale. This is not an accurate method to determine an object’s mass. Mass is more fundamental than weight; because mass is the measure of the amount of matter in an object and depends only on the number and kind of atoms in the object. Weight, on the other hand, is a measure of the gravitational force acting on an object. There are places where a massive object has no weight as in space, hence weight depends on an object’s location – Earth is by far the most common location considered when weight is discussed. That is why we often confuse the terms weight and mass.
Mass is the measure of the amount of matter in an object and weight is the force exerted by gravity on an object. A person has the same mass at all times, no matter where the person is located. However, the weight of the person can change drastically depending on where the person is. A person weighs more at sea level than he/she does on top of a mountain because the pull of gravity is greater at sea level (closer to the center of the Earth) than it is on the top of a mountain. Similarly, a person weighs more on the Earth than he or she does on the Moon because the force of gravity on Earth is greater (about 6 times) than that on the Moon.
What is the difference between mass and weight?
The correct answer is C. It is important to understand that mass never changes, whereas weight is simply the gravitational force exerted on a mass.
By the time he was twenty-four years old, Sir Isaac Newton had developed the three laws of motion, the cornerstone of all of physics.
Newton’s First Law of Motion states that every object at rest will remain at rest, and any object in motion will remain in motion (in a straight line at a constant speed) unless acted upon by an outside force.
In other words, an object tends to remain in its state of motion or non-motion unless a non-zero force acts upon it. A book on your desk, for example, is in a state of rest unless it is moved in some way. Now consider if the book was in motion on your desk. Let’s say you exerted a quick force on your book trying to slide it off the end of your desk. Most likely, the book would come to a stop before it fell off. This is because of a large frictional force between the book and the desk. The moment you let go of the book, it is in motion and tries to stay in motion, but because of the outside force of friction that acts on the book after you let go, it stops. Now imagine you took your book to the arcade and slid it across an air hockey table. The book would slide easily across the table in a straight line, probably hitting the side before it stops because there is less friction.
Whether an object is in motion or not, it resists any change to that state of motion. This is called inertia, the tendency of an object to resist any change in its motion. Newton’s first law of motion is also called the law of inertia. Some objects have more inertia than other objects. For example, if you try to push an elephant and then try to push a beetle, you quickly realize that the elephant is much harder to push because it is more massive (i.e., it has more mass). Likewise, when you try to stop an elephant, it is much harder to stop than the beetle. The greater the mass of an object, the greater its inertia, and the greater the force needed to change its motion.
Acceleration describes the rate at which the velocity of an object changes a = v / t. We also know that if we apply a non-zero force to an object, its state of motion changes. The most popular sport in the world gives us a great example. Consider a soccer ball at rest. Apply a force with your foot and it starts to move. Since the ball was not moving before you kicked it, it accelerated, or changed its velocity. The ball accelerates each time you kick it; force causes acceleration. It is also important to remember that velocity, unlike speed, includes both speed and direction. Hence an object that changes direction at a constant speed is also accelerating.
Now if you kick the soccer ball and kick the goal post, you will find that the ball accelerates and moves easily, while the goal post is much harder to accelerate and move by applying a force. Now, kicking goal posts is not recommended, but it makes a good example for the observation that for any given force (e.g., your kick), the acceleration produced in another object (e.g., the ball or the goal post), is inversely proportional to the mass of that object. Newton came up with one of the most important laws of nature ever proposed, the Second Law of Motion, which states: When a non-zero force is applied to a body, that body is accelerated in the direction of the applied force at a rate directly proportional to the applied force and indirectly proportional to the mass of the body. In equation form, the second law is:
Or, more commonly:
If a force of 2000 Newtons is applied to a 1,000 Kg car, what is the car’s acceleration?
The correct answer is D and can be obtained by dividing the force by the mass.
Newton also realized that force is not just a single entity, but is an interaction between two objects. Suppose you pound a nail into some wood with a hammer. You strike the nail with the hammer and the nail goes into the wood because of the force exerted on the nail by the hammer. That is only half of the story. What stopped the hammer from moving? The nail actually exerted a force on the hammer to stop its motion. So there was an interaction of two forces: the hammer on the nail, and the nail on the hammer.
Newton realized that forces come in pairs, which brought him to his third law of motion. Newton’s Third Law of Motion states that when one object exerts a force on another object, the second object exerts an equal and opposite force on the first object. The key idea here is that each force is a part of a system and for every action there is an equal and opposite reaction.
It is important to emphasize here the concept of action/reaction pairs, meaning two objects. If object A acts on object B, then the reaction is object B acting on object A. The reaction is never caused by a third object. For example, if a 150 pound person is standing on a floor, Earth’s gravity is exerting a downward force of 150 pounds on the person. The reaction to that force, required by Newton’s third law, is the person’s gravity pulling up on the Earth with a force of 150 pounds. These forces (Earth on person and person on Earth) form an action reaction pair. The floor also exerts an upward force of 150 pounds on the person, but that is not the reaction to the Earth pulling the person down. Not all equal and opposite forces form the action reaction pairs required by Newton’s third law.
We all know how objects fall to Earth because of gravity, and that gravity is what holds water in a glass. Gravity is the main interaction between objects. Newton made key observations about how gravity behaves between all objects. He discovered that gravity is universal – it exists everywhere, between all objects, and it depends on the masses of the objects and the distance between them.
Newton’s Universal Law of Gravitation states that all objects attract all other objects with a force that is proportional to the product of the mass of the objects, and is inversely proportional to the square of the distance between them. Stated in equation form, this law is:
Newton recognized that the greater the masses of two objects, the greater the force of attraction between them. Moreover, the closer the two objects are to each other, the greater the force of attraction –by the square of that distance.
Newton also realized that all objects in the universe are affected by gravity and their gravitational forces act everywhere in the universe, not just on Earth. The force that makes an apple fall to the ground is the same force that keeps the planets in orbit around the sun and is also the same force that would allow a leaf in California to attract and potentially come into contact with a feather in New York (if there were no other forces like friction or objects in the way to prevent that from happening, no matter the object’s sizes or locations). Nonetheless, the attractive force between the leaf and the feather (and ALL objects everywhere) is still there. Most of the time, however, this force is only great enough to be noticed when at least one of the objects is massive.
Now imagine a man flying in a hot air balloon 20 meters above the ground. Is the force of attraction between the man and the center of the Earth the same as when he stands on the Earth? No. The force of attraction between the man and the center of the Earth (his weight) when he is standing on the ground is more than when he is in the hot air balloon 20 meters high.
The fact that gravity is inversely proportional to the square of the distance between the objects in questions is the key here. When the man is standing on the ground, the distance between him and the center of the Earth is less than when he is 20 meters high in the hot air balloon. His mass and the Earth’s mass are the same whether he is up in the balloon or not. Because he is farther from the center of the Earth when he is up in the balloon, the force between him and the center of the Earth is less than when he is on the ground. This difference in force is very slight because the difference in distance is very slight, but it does exist. However as the distance between the man and the earth increases, the weight of the man decreases, eventually leading to “weightlessness” of astronauts in space.
Which one of the following equations correctly describes the mathematical nature of the law of universal gravitation?
The correct answer is C. Gravitational force is best described as the product of the masses of the objects divided by their distance squared.
Momentum is the characteristic of a moving object that makes it difficult to stop. Consider a bicycle moving at 1 km per hour and a train moving at 1 km per hour. The train has the most momentum and is much harder to stop because it has so much more mass than the bicycle: or consider two identical automobiles, one of them is moving at 1 km per hour and the other automobile is moving at 100 km per hour. The faster moving automobile has more momentum and is much harder to stop because it has a higher velocity. So momentum has something to do with both mass and velocity. The momentum (p) of an object is defined as the product of the mass (m) and velocity (v) of the object, or:
p = mv
What is the momentum of a 50 Kg object traveling at 25 m/s?
The correct answer, A, is obtained by multiplying the mass of the object by its velocity.
Momentum and Newton’s third law of motion lead us to another fundamental law of nature, the Conservation of Momentum. The Law of Conservation of Momentum states that in the absence of external forces, the momentum of a system is conserved – it never changes. Obviously, there is an intimate relationship between inertia and momentum.
The momentum of a system never changes unless it is acted on by outside forces. An isolated system will always have the same momentum before an interaction as it does after the interaction. Use this fact to help answer the following question.
A 1,000 Kg automobile moving with a velocity of 50 m/s collides with another 1,000 Kg automobile at rest, and they get stuck together from the impact. Immediately after the collision (and ignoring the effects of friction), how fast will the two automobiles be traveling?
The correct answer is B. Multiplying the masses and the velocities before the collision and setting them equal to the product of the masses and velocities after the collision, the equation for the speed of the two automobiles together gives 25 m/s. Answer A is incorrect since the momentum before the collision was not zero.