Newton's First Law of Motion: Difference between revisions

Revision as of 13:05, 2 August 2019

This page describes Newton's first law of motion, the first of his three famous laws of motion published in his work Principia Mathematica.

The Main Idea

Newton's First law states that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and direction of travel unless the object is acted upon by an unbalanced external force.

Also called the Law of Inertia, the law states that it is the natural tendency for objects to remain on their current course.

A Mathematical Model

The first law states that if the Net Force acting on the object is zero, then its velocity [math]\displaystyle{ \vec{v} }[/math] will not change over time. Velocity is a vector, which has both direction and magnitude, therefore if the Net Force is zero, neither the direction or magnitude can be changing.

This idea can be expressed in the following manner:

[math]\displaystyle{ \sum \mathbf{\vec{F}} = 0\; \Leftrightarrow\; \frac{\mathrm{d} \mathbf{\vec{v}} }{\mathrm{d}t} = 0. }[/math]

Newton's first law applies to:

1) Objects at rest ([math]\displaystyle{ |\vec{v}| = 0 }[/math]), which will stay at rest unless a nonzero force acts upon it.

2) Objects in motion ([math]\displaystyle{ |\vec{v}| \neq 0 }[/math]), which will continue to be in motion with the same velocity, proceeding in the same straight line, unless a nonzero force acts upon it.

Examples

Because of the qualitative nature of Newton's first law, some of these example problems are conceptual questions rather than mathematical calculations.

Simple

Question 1: Suppose you want to push a box across a table in a straight line at a constant speed. What force, if any, would you have to exert on the box? (Describe it qualitatively- not enough information is supplied for a numerical answer.)

Answer: The moving box would experience 3 forces (besides any you exert on it): gravity, normal force from the table, and friction with the table and air. Gravity points downwards, normal force points upwards, and friction opposes the direction of motion. Because of the nature of normal force, the normal force takes on whatever magnitude necessary to cancel gravity. The only unbalanced force is therefore friction. Since your objective is to keep the box moving in a straight line at a constant speed (that is, at a constant velocity), the net force acting on the box must be 0 according to Newton's first law. The force you exert should therefore balance the friction force by being equal in magnitude and opposite in direction.

Question 2: Is a change in position an indicator of interaction?

Answer: On its own, a change in position is not enough to indicate an interaction because an object can have a nonzero velocity (that is, have a changing position) even with no forces acting on it, so long as that velocity is constant. With some additional information, however, a change in position can indicate an interaction. For example, if an object is initially at rest and is later found at another position, its velocity must have changed and it must have been acted on by a nonzero unbalanced external force.

Medium

Question: A 16kg traffic light is suspended by two cables, each 22[math]\displaystyle{ ^\circ }[/math] from horizontal, as shown below:

What is the tension in each of the cables?

Solution: Because the traffic light is at rest and not accelerating, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the traffic light are gravity and tension in the 2 cables. The horizontal components of the cables' tension forces must be equal in magnitude, or the traffic light would be accelerating to the left or the right. Combining that information with the fact that the two cables are inclined by the same amount leads to the conclusion that the tension in the two cables must be the same. Finally, we know that the combined vertical components of the two cables' tension forces must equal the traffic light's weight, or the light would be accelerating vertically. This allows us to create the following equation:

[math]\displaystyle{ 2T\sin(22) = 16*9.8 }[/math]

[math]\displaystyle{ T = \frac{16*9.8}{2\sin(22)} = 209.3 }[/math]N.

Difficult

Question: Suppose there exists a car of mass 9000 kg that is moving at a constant speed of 90 m/s in the positive x direction. If you know that the wheels provide a force of 1000 N to the right, what is the frictional constant and the normal force?

Solutions: First off, we need to recognize that there is no change in velocity, since the question so clearly mentions the word constant. Therefore, the net force is zero. This means the net force in the horizontal and vertical directions is zero. If we begin with the vertical component, we know that the normal force must equal the gravitational force. If not, the car would be moving towards the ground. So 9.8*9000 = Normal Force. This means, the normal force equals 88200 N. Now, to find the frictional force, we know that we are providing a force of 1000 N to the right. That must mean that to make the net horizontal force zero, the frictional force must be 1000 N to the left. Now, frictional force = frictional constant*normal force. So, constant=friction force/normal force. Constant= 1.

Connectedness

This topic is connected to every aspect of life. Every time you get in a car or drop something on the floor or trip over a rock Newton's First Law is demonstrating itself to you. The connections of this topic to the real world is an endless list of possibilities.

Some magicians often have "tricked" their audiences into believing their great powers when in reality, it is nothing more than the skillful manipulation of Newton's First Law. For example, when a magician pulls out a tablecloth from plates on the table and the plates maintain their initial state of rest without any change in their velocities, some people might be fooled into believing in magic. However, any admirer of Newton would know that this is simply a manipulation of Newton's First Law. The object (the plates) were not in motion, and because the tablecloth was pulled out in such a manner that it does not exert a force onto the plates, the plates do not change velocities.

In space, there are small objects that are floating in a straight line. They are far enough from any large objects that no gravitational force exists to effect their motion. So, because there is no external force and the object was moving, it keeps on moving in a straight line indefinitely. Although modern astronomers would argue that the object would eventually come in contact with another object of great size that would exert a significant gravitational force onto this object, other astronomers could argue about the nature of the universe and the possibility that the object could be moving at the edge of the universe where it is moving at the same speed as the expansion of the universe and therefore could indeed move forever without any change in its velocity.

History

This theory was originally discovered by Galileo who conducted experiments on the concepts of inertia and acceleration due to gravity. Galileo studied the movement of balls on smooth and rough surfaces, developing the idea of friction. Isaac Newton further studied these concepts and ideas and presented his 3 Laws of Motion. The first of these 3 laws, as we know, stated that an object in motion will stay in motion with the same speed and direction until an unbalanced force acts on it. And with the absence of friction or other forces, an object will continue moving forever.

From the original Latin of Newton's Principia: Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

Translated to English, this reads: "Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed."

Aristotle, the Greek who had an opinion on everything, believed that all objects have a natural place. Heavy objects wanted to be at rest on the Earth and light objects like smoke wanted to be at rest in the sky. He even went so far as to hypothesize that stars belonged only in the heavens. He thought that the natural state of objects was at rest and that nothing could keep moving forever without an external force. He did not believe that an object, without any external forces, could keep moving forever.

Galileo, a more enlightened man, believed that although an outside force was needed to change the velocity of an object, no force was necessary to maintain its object. It could keep moving forever if nothing acted on it.

Newton, who formally stated the law in the fancy language of Latin and whose name is attached to the very law, actually did nothing more than simply restate the law of inertia which Galileo had already described. He even gave the appropriate credit to Galileo, but to this day, we refer to this law not as Galileo's First Law, but as Newton's.

Page Created by: Brittney Vidal November 10, 2015 <-- For Credit

Page Edited by: Vivekanand Rajasekar November 27, 2015 <-- For Credit

Page Edited by: Raj Patel April 9, 2017 <-- Not For Credit

Interactions

@@ Line 44: / Line 44: @@
 What is the tension in each of the cables?
-Solution: Because the traffic light is at rest and not accelerating, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the traffic light are gravity and tension in the 2 cables. The horizontal components of the cables' tension forces must be equal in magnitude, or the traffic light would be accelerating to the left or the right. Combining that information with the fact that the two cables are inclined by the same amount leads to the conclusion that the tension in the two cables must be the same. Finally, we know that the combined vertical components of the two cables' tension forces must equal the traffic light's weight, or the light would be accelerating vertically. This allows us to create the following equation:
+Solution: Because the traffic light is at rest and not accelerating, by Newton's first law, any forces acting on it must be balanced (that is, the net force acting on it must be 0). The forces acting on the traffic light are gravity and tension in the 2 cables. The horizontal components of the cables' tension forces must be equal in magnitude, or the traffic light would be accelerating to the left or the right. Combining that information with the fact that the two cables are inclined by the same amount leads to the conclusion that the tension in the two cables must be the same. Finally, we know that the combined vertical components of the two cables' tension forces must equal the traffic light's weight, or the light would be accelerating vertically. This allows us to create the following equation:
 <math>2T\sin(22) = 16*9.8</math>

Newton's First Law of Motion: Difference between revisions

Revision as of 13:05, 2 August 2019

Contents

The Main Idea

A Mathematical Model

Examples

Simple

Medium

Difficult

Connectedness

History

See Also

Further reading or exploring

External links

References

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