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Laws of Inertia

Topics: Force, Mass, Inertia, Classical mechanics / Pages: 8 (1869 words) / Published: Jan 4th, 2014
Inertia

(Law of Inertia)

Name _____________________ Section _________ Date ______

The law of acceleration explains how a net force makes a mass accelerate. It shows how the magnitude of the acceleration depends on the magnitude of the force (directly proportional) and on the magnitude of the mass (inversely proportional). Acceleration happens only when there is an unbalanced force.

Where All Forces Are Balanced

No change of velocity occurs when the forces acting a body are balanced. You can apply two or more forces on the same body but it does not necessarily mean that there will be acceleration. There will be no change in the original velocity of a body if there are no unbalanced forces acting on it. It means that a body at rest (technically at the velocity of 0 m/s) will maintain that velocity unless there is an exteranal unbalanced force or net force acting on it. The mass will stay in its original state of motion, that is being at rest.

We can add more forces but if these forces cancel each other, the velocity will remain at zero. There are large forces. Yes. Nevertheless, because they amount to zero, there is no change of velocity, no acceleration. The body will remain at rest.

In the same way, a body that is already in motion will not change its velocity unless there is an unbalanced force applied to it. Take a block that is freely sliding over a smooth surface. It is moving at 4 m/s. If no force acts on it, the velocity will still be the same after some time. It will go on and on at the same velocity.

Once a body is set into motion, the body preserves that motion of itself without need of any other force to keep on going at the same speed and in the same direction. You will recall that when a bowler rolls the ball on the lane, the ball just goes on by itself once it leaves the hand of the player. You throw a Frisbee and it goes on by itself until it is caught by your sister. That is the way an archer shoots an arrow. The bow sets it into motion and then the arrow flies by itself. A car that is moving at a certain speed will not stop right after the driver stops giving gas. Don’t step on the brakes and put the gears to neutral, does your car just stop. It tends to go on by itself. This is a property of masses. They tend to move on at the same velocity once they are put into motion. This is an innate tendency of mass or bodies. This is the property or tendency to stay at rest (when they are at rest) and to keep moving on a constant velocity (when they are in motion). Rest and motion will be changed only if some external force is given to the body. Force is not needed to maintain rest, force is not needed to maintain motion. The mass does not want to change what it is doing whether it is resting or moving. It wants to preserve that same status. We repeat, this behavior is an inherent property of a mass.

How do we describe people who behave like that? Yes, lazy. Their attitude is called laziness. Yes, masses possess laziness. Why are some people lazy? We don’t know. They just happen to be like that. It is part of their character. Masses are that way too because that is their property. Laziness connotes a negative attitude. Isaac Newton did not want to use the English word “laziness”. Instead, he chose a Latin word to cloak it. The word is INERTIA. Do you want to know the original meaning of inertia? Well, it means laziness. Sounds crazy! You see when people read the word INERTIA, they do not immediately think of laziness. It sounds like some big scientific word. No, it simply means laziness. And for Physics, it is the laziness of a mass to change whatever it is doing. If it is at rest, it is lazy to move. If it is moving, it is lazy to change that and it just wants to keep on moving in the same direction at the same velocity.

Inertia is defined as the tendency of a body to continue in its original state of motion, unless some external force acts on it. (This concept was first conceived by Rene Descartes. The Galileo Galilei used the concept in his motion studies and finally Isaac Newton crystallized it into the Law of Inertia.) The idea of inertia means that you do not need a force to keep a body moving at constant speed. We have already given examples above but sometimes it is still difficult to grasp this idea because of some of our daily experiences.

When you cycle on a level road, you have to peddle steadily, that is exert a constant force, to keep the bike moving at a constant speed. If you stop pedaling, the bicycle slows down. To accelerate, you must peddle harder. From this and many other daily experiences, it seems that force is needed to keep a body moving. But this is wrong! Over 2000 years ago, Aristotle first suggested that constant force was needed to keep a body moving at constant speed and that extra force was needed for acceleration. There many peculiar arguments to defend this idea.

In the sixteenth century Galileo worked out a thought experiment. A metal sphere is released from position A to run down a smooth incline ( a bent rail). When the rail is bent long ABC, the ball rises up to C, which is

nearly the same height as A. (The slight difference is height is due to friction between the ball and the rail. Then the rail is adjusted. With the rail bent along ABD and ABE, the ball again rises to nearly to the same height as A. It is as if the ball “remembers” the height. It does not stop until it reaches that height A. What happens if the rail is bent along ABF where BF is horizontal? What do you think? Of course, the ball would never be able to rise up to the same height as A. And it would not stop moving until it gets to that height. Galileo argued that, in the absence of friction, it would move on forever at a constant speed along a straight line. (This was only a “thought experiment.”)

Galileo’s argument in the thought experiment about inclined rails was based on his observation of a swinging pendulum. If a pendulum bob is pulled to one side and released, it will swing to the other side, rising to the same height as before. A pin was then placed in the path of the bob. The pin changes the path of the swing. But even then, the bob rises to the same height as before. (This is the pin-and-pendulum experiment.) In this experiment, very little friction acts on the bob.

In these experiments, Galielo did not try to explain why a body keeps on moving at constant speed along a straight line. He simply pointed out that it is natural for a moving body to do so, just as it is natural for a stationary body to remain at rest. (This idea of motion is called Galileo’s law of inertia. Galileo’s studies were further developed by Newton who published his own ideas in the book Principia Mathematica Philosophiae Naturalis in 1687.

Mass and Inertia (Inertial Mass)

There are two stationary masses, one is large (5 kg) and the other is small (1 kg). Which of the two will be easier to push into motion? Right, the small one. Why? It is small. The small mass tends to remain at rest because it has inertia. To push it, you need to overcome inertia, small amount of inertia. The large object is harder to push, naturally. It has a large amount of inertia. Why? Because it has a larger mass, you have to overcome greater inertia.

Imagine that these two objects are already in motion and you have to stop them. Would you say that it will be more difficult to stop the large mass or would the effort be just the same for both masses? It requires more effort to stop the large mass, because it has a greater tendency to keep on moving. The small mass has less inertia or tendency to move on.

What are you saying here? If the mass is large, its inertia is large too. If the mass is small, there is small inertia. On the other hand, a body that has great inertia means the mass is large. When you encounter little inertia, then the mass involved is small. From where does the inertia come? Right, from the mass itself. So the amount of inertia is the amount of mass and the amount of mass is the amount of inertia. Inertia is the measure of the mass. Mass is the measure of inertia. What is the conclusion? Mass is the amount of inertia in a body. Inertia is the amount of mass in a body. This brings now to yet another definition of mass. You surely know that mass is the amount of matter present in a body. You can now define mass as the amount of inertia possessed by the body.

Questions:

1. If you are standing in a bus, what happens to you when a) the bus starts moving, b) stops moving and c) turns a corner?
2. A piece of cardboard rests on top of a jar. On the cardboard, there lies a coin. What happens when the cardboard is suddenly flicked off sharply with a finger?
3. Explain why the seat belt and the head rest are useful devices in a car.
4. Spacecraft can travel far out in space with a constant speed along a straight line, even if no rocket propels it along.
5. A ball is rolling on a table top with a speed of 1.5 m/s toward the edge of the table. What happens when the speeding ball reaches the edge?
6. A helicopter is flying at constant speed over the desert to drop a box of supplies to a man on the ground. When the chopper is directly over the man, the pilot releases the box. Will the box land right where the man is?
7. Can a runner coming in a great 9 m/s immediately stop right on the finish line?
8. An archer stands on the bed of a truck moving at 40 km/h. He sees a duck flying overhead, aims and when the duck is directly overhead, he shoots the arrow. Predict what happens to the duck and to the arrow.
9. The are thousands of tiny round pellets evenly spread on a metal tray. A block of wood rests on the pellets. What happens if you quickly pull on one side of the tray.
10. Why is a constant push no longer needed to bring the ball from the kick of player to the goal? If the kick gives it a velocity of 40 m/s, at what velocity will the goalkeeper catch it?

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