other. The reaction force is responsible for the motion of the person or the car. These
forces depend on friction; however, if a person or car is on ice, there will be no
motion because of failure to produce the needed reaction force.
It is important to point out that Robert Hooke (1687) published the third law for
deformable bodies as F ¼ k u, where k is the stiffness of a one-dimensional spring
and u is the displacement response in the direction of the force. “Hooke stated in his
1687 work that he was aware of the law in 1600, which is long before Newton
published his Principia” (Robert Hooke’s Wikipedia page).
“In their original form, Newton’s laws of motion are not adequate to characterize the motion
of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalization
of Newton’s laws of motion for rigid bodies called Euler’s laws of motion, later applied as
well for deformable bodies assumed as a continuum. If a body is represented as an
assemblage of discrete particles, each governed by Newton’s laws of motion, then Euler's
laws can be derived from Newton’s laws. Euler’s laws can, however, be taken as axioms
describing the laws of motion for extended bodies, independently of any particle structure
(Lubliner 2008)” (Leonard Euler Wikipedia page).
2.1.4 Range of Validity of Newton’s Universal Laws
of Motion
“Newton’s laws were verified by experiments and observations for over 200 years,
and they are excellent approximations at the scales and speeds of most of the motions
we observe in daily life. Newton’s laws of motion, together with his law of universal
gravitation and the mathematical techniques of calculus, provided for the first time a
unified quantitative explanation for a wide range of physical phenomena.
These three laws hold to a good approximation for macroscopic objects under
everyday conditions. However, Newton’s laws are inappropriate for use in certain
circumstances, most notably, at very high speeds (in special relativity, the Lorentz
factor must be included in the expression for momentum along with the rest mass
and velocity) or at very strong gravitational fields. Therefore, Newton’s laws cannot
be used to explain phenomena such as conduction of electricity in a semiconductor,
optical properties of materials, errors in nonrelativistically corrected GPS systems,
and superconductivity. Explanation of these phenomena requires more sophisticated
physical theories, including general relativity and quantum field theory.
However, in quantum mechanics, concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that
are much lower than the speed of light, Newton’s laws are just as exact for these
operators as they are for classical objects” (Anon 2020).
2.1 Newton’s Universal Laws of Motion
11
forces depend on friction; however, if a person or car is on ice, there will be no
motion because of failure to produce the needed reaction force.
It is important to point out that Robert Hooke (1687) published the third law for
deformable bodies as F ¼ k u, where k is the stiffness of a one-dimensional spring
and u is the displacement response in the direction of the force. “Hooke stated in his
1687 work that he was aware of the law in 1600, which is long before Newton
published his Principia” (Robert Hooke’s Wikipedia page).
“In their original form, Newton’s laws of motion are not adequate to characterize the motion
of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalization
of Newton’s laws of motion for rigid bodies called Euler’s laws of motion, later applied as
well for deformable bodies assumed as a continuum. If a body is represented as an
assemblage of discrete particles, each governed by Newton’s laws of motion, then Euler's
laws can be derived from Newton’s laws. Euler’s laws can, however, be taken as axioms
describing the laws of motion for extended bodies, independently of any particle structure
(Lubliner 2008)” (Leonard Euler Wikipedia page).
2.1.4 Range of Validity of Newton’s Universal Laws
of Motion
“Newton’s laws were verified by experiments and observations for over 200 years,
and they are excellent approximations at the scales and speeds of most of the motions
we observe in daily life. Newton’s laws of motion, together with his law of universal
gravitation and the mathematical techniques of calculus, provided for the first time a
unified quantitative explanation for a wide range of physical phenomena.
These three laws hold to a good approximation for macroscopic objects under
everyday conditions. However, Newton’s laws are inappropriate for use in certain
circumstances, most notably, at very high speeds (in special relativity, the Lorentz
factor must be included in the expression for momentum along with the rest mass
and velocity) or at very strong gravitational fields. Therefore, Newton’s laws cannot
be used to explain phenomena such as conduction of electricity in a semiconductor,
optical properties of materials, errors in nonrelativistically corrected GPS systems,
and superconductivity. Explanation of these phenomena requires more sophisticated
physical theories, including general relativity and quantum field theory.
However, in quantum mechanics, concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that
are much lower than the speed of light, Newton’s laws are just as exact for these
operators as they are for classical objects” (Anon 2020).
2.1 Newton’s Universal Laws of Motion
11