Question about Newton's Laws?

Question

I've been stuck on this question for an hour now and it seems like a trick question, but I'm still not sure where to go with it.

Newton's first law states that an object will move with a constant velocity if nothing acts on it. This seems to contradict our everyday experience that all moving objects come to rest unless something acts on it to keep it going. Does our everyday experience contradict one of Newton's Laws? If it does not, explain the apparent contradiction. If it does, explain why we bother to teach Newton's first law anyway.

Thanks!

Answer 1

Newton's laws of motion are three physical laws that form the basis for classical mechanics. They are:

1.In the absence of net external force, a body either is at rest or moves in a straight line with constant velocity.
2.Force is proportional to mass times acceleration (when proper units are chosen, F = ma). Alternatively, force is proportional to the time rate of change of momentum.
3.Whenever a first body exerts a force F on a second body, the second body exerts a force -F on the first body. F and -F are equal in size and opposite in direction.
These laws describe the relationship between the forces acting on a body to the motion of the body. They were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, first published on July 5, 1687.[1] Newton used them to explain and investigate the motion of many physical objects and systems.[2] For example, in the third volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion.

Contents [hide]
1 The three laws
1.1 Newton's first law
1.1.1 History of the first law
1.2 Newton's second law
1.2.1 Impulse
1.2.2 Variable-mass systems
1.3 Newton's third law: law of reciprocal actions
2 Importance and range of validity
3 Relationship to the conservation laws
4 See also
5 Notes
6 References and notes
7 Further reading
8 External links


[edit] The three laws
First law
There exists a set of inertial reference frames relative to which all particles with no net force acting on them will move without change in their velocity. This law is often simplified as "A body persists its state of rest or of uniform motion unless acted upon by an external unbalanced force." Newton's first law is often referred to as the law of inertia.
Second law
Observed from an inertial reference frame, the net force on a particle is equal to the time rate of change of its linear momentum: F = d(mv)/dt. This law is often stated as, "Force equals mass times acceleration (F = ma): the net force on an object is equal to the mass of the object multiplied by its acceleration."
Third law
Whenever a particle A exerts a force on another particle B, B simultaneously exerts a force on A with the same magnitude in the opposite direction. The strong form of the law further postulates that these two forces act along the same line. This law is often simplified into the sentence, "To every action there is an equal and opposite reaction."
In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation: one can consider the laws to be a definition of these quantities. Notice that the second law only holds when the observation is made from an inertial reference frame, and since an inertial reference frame is defined by the first law, asking a proof of the first law from the second law is a logical fallacy. At speeds approaching the speed of light the effects of special relativity must be taken into account.[note 1]


[edit] Newton's first law
Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare. 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.[3]

Newton's first law is also called the law of inertia. It states that if the vector sum of all forces (that is, the net force) acting on an object is zero, then the acceleration of the object is zero and its velocity is constant. Consequently:

An object that is not moving will not move until a net force acts upon it.
An object that is moving will not change its velocity until a net force acts upon it.
The first point needs no comment, but the second seems to violate everyday experience. For example, a hockey puck sliding along ice does not move forever; rather, it slows and eventually comes to a stop. According to Newton's first law, the puck comes to a stop because of a net external force applied in the direction opposite to its motion. This net external force is due to a frictional force between the puck and the ice, as well as a frictional force between the puck and the air. If the ice were frictionless and the puck were traveling in a vacuum, the net external force on the puck would be zero and it would travel with constant velocity so long as its path were unobstructed.

Implicit in the discussion of Newton's first law is the concept of an inertial reference frame, which for the purposes of Newtonian mechanics is defined to be a reference frame in which Newton's first law holds true.

There is a class of frames of reference (called inertial frames) relative to which the motion of a particle not subject to forces is a straight line.[4]

Newton placed the law of inertia first to establish frames of reference for which the other laws are applicable.[5][4] To understand why the laws are restricted to inertial frames, consider a ball at rest inside an airplane on a runway. From the perspective of an observer within the airplane (that is, from the airplane's frame of reference) the ball will appear to move backward as the plane accelerates forward. This motion appears to contradict Newton's second law (F = ma), since, from the point of view of the passengers, there appears to be no force acting on the ball that would cause it to move. However, Newton's first law does not apply: the stationary ball does not remain stationary in the absence of external force. Thus the reference frame of the airplane is not inertial, and Newton's second law does not hold in the form F = ma.[note 2]


[edit] History of the first law
Newton's first law is a restatement of what Galileo had already described and Newton gave credit to Galileo. It differs from Aristotle's view that all objects have a natural place in the universe. Aristotle believed that heavy objects like rocks wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. However, a key difference between Galileo's idea and Aristotle's is that Galileo realized that force acting on a body determines acceleration, not velocity. This insight leads to Newton's First Law—no force means no acceleration, and hence the body will maintain its velocity.

The law of inertia apparently occurred to several different natural philosophers and scientists independently. The inertia of motion was described in the 3rd century BC by the Chinese philosopher Mo Tzu, and in the 11th century by the Muslim scientists Alhazen[6] and Avicenna.[7] The 17th century philosopher René Descartes also formulated the law, although he did not perform any experiments to confirm it.

The first law was understood philosophically well before Newton's publication of the law.[note 3]


[edit] Newton's second law
Newton's Latin wording for the second law is:

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

This was translated quite closely in Motte's 1729 translation as: