Basic Physics Of Quantum Theory, The. Basil S Davis
and creatures that flew through the air all acted as though the earth were stationary. It required Newton to explain how these phenomena could be consistent with a rotating earth.
After Copernicus, astronomers abandoned Ptolemy’s model and made further observations that both confirmed and refined Copernicus’ model.
Tycho Brahe (died 1601) constructed an extremely accurate observatory. He recorded the position (i.e. the angular position of a celestial object when viewed from a point on the ground) of the heavenly bodies at different times over a period of several years.
Johannes Kepler (died 1630) made use of Brahe’s data and found that they conflicted slightly with the data used in support of Ptolemy’s and Copernicus’ models. Kepler found that Brahe’s data could be explained by suggesting that the earth and the planets did not travel round the sun in perfect circles, but rather in ellipses (oval paths), with the sun at one focus of the ellipse.
With the invention of the telescope, Galileo Galilei (died 1642) was able to show that the planet Venus showed all the phases — full, gibbous, half, crescent — as the moon. This was perfectly explainable on Copernicus’ heliocentric model, but not on Ptolemy’s geocentric model. Ptolemy’s model did not allow for a full phase of Venus to be visible from earth. Thus there was unquestionable evidence — in addition to Brahe’s observations and the calculations of Kepler — that the planets do indeed orbit the sun.
A year after Galileo’s death saw the birth of Isaac Newton who became the father of what we today call Physics in the modern sense of the term. Newton used the theories of Kepler and the observations of Galileo to establish a mathematical description of physics which still endures today, though it has been greatly modified by Albert Einstein’s theory of Relativity and the Quantum theory developed by several physicists of the early twentieth century.
2.5Newton’s laws
Several Greek philosophers made significant contributions to our understanding of nature, but it was Aristotle who drew up a system for understanding fundamental physical phenomena. Aristotle believed — as did most Greek philosophers — that all matter was composed of the elements: earth, air, water, fire and ether. Vertical motion was natural. Solid objects fell to the ground because they sought to be close to the earth, since they were also made of earth. Liquids fell or flowed downwards because they sought to be united to the seas, the domain of the element called water. Flames shot upwards because the domain of fire was above. The purpose of all natural motion was goal oriented. Horizontal motion, on the other hand, was violent, and needed an agent to sustain it. The motion of the stars was circular, because this was the property of ether.
But Aristotelian physics was not based on carefully controlled observation. Laboratory experiments showed that bodies had this property called inertia which would cause a moving body to continue its motion in the absence of friction or air resistance.
Newton raised the concept of inertia to the status of a law of physics. He was thus able to show that all motion could be explained on the basis of his three laws of motion:
First Law:
Every object remains at rest, or moves with a constant speed in a straight line, unless compelled to do otherwise by an external force.
As the earth rotates, the air that is close to the ground also moves with the same speed as the ground. Every object that floats or flies through the air is also carried along with the motion of the earth. Inertia keeps everything going together. So we cannot tell from an observation of the atmosphere that the earth is in motion, any more than we can tell that an airplane is moving by observing an object that is dropped inside the plane. Of course, because the motion of the earth is a rotation and not a simple translation along a straight line, there are other factors that give rise to atmospheric phenomena such as hurricanes, and it is these that reveal the rotation of the earth.
Second Law:
An external force F applied to an object of mass m would impart an acceleration a to the object in the direction of the force such that F = ma.
Acceleration is not just increase of speed, but any change of velocity in magnitude or direction. So an object moving on a circular path is accelerating because its direction of motion is changing. It can be shown with some calculation that an object moving along a circle of radius r with a constant speed v experiences an acceleration of magnitude v2/r directed towards the center of the circle.
An important quantity in the study of motion is the momentum of an object, written as p and defined as the product of mass and velocity: p = mv. Acceleration is the rate of change of velocity. So the product ma is the rate of change of momentum. So Newton’s Second Law can be stated as: Force = Rate of change of momentum.
Exercise 2.2.
(a) A car of mass 1500 kg accelerates from rest to a speed of 60 kmph in 10 seconds. Find the average force applied on the car by the engine. (Convert kmph into meters per second. Remember, average acceleration = change of velocity divided by time.)
(b) Taking the distance of the earth to the sun as 150,000,000 km find the circumference of the earth’s orbit in meters. Hence find the speed of the earth as it travels through space. Use the result of Exercise 2.1 (b).
(c) Find the acceleration of the earth as it orbits the sun.
Third Law:
When an object A applies a force on an object B, the object B simultaneously applies an equal and opposite force on object A.
The Third Law explains why we do not go through the floor. Our weight applies a force on the floor, and the floor applies an equal and opposite force — called the normal force — on our feet.
These laws have successfully explained horizontal motion. What about vertical motion? According to the Second Law an accelerating body must be driven by a force. So if an apple accelerates to the ground it is because there is a force acting upon it. Moreover, this law also states that the force is proportional to the acceleration. Not all bodies are pulled to the earth by the same force. Some objects are heavier than others. But heavier and lighter objects fall at the same acceleration in the absence of air resistance. The Second Law can also be written as a = F/m. The acceleration equals the force divided by the mass. Since all falling objects accelerate at the same rate in a vacuum where there is no air resistance, Newton’s Second Law indicates that there must be a force — the force of gravity — acting on an object that is proportional to the mass of the object. The greater the mass, the greater the force, and so the ratio of force to mass stays constant.
So the force exerted by the earth on an apple is proportional to the mass of the apple. Newton’s Third Law requires that if the earth exerts a force on the apple, the apple must exert an equal and opposite force on the earth. Through an argument from symmetry it follows that the force exerted by the apple on the earth should be proportional to the mass of the earth. So this suggests that the mutual force of attraction between two objects should be proportional to the product of the masses of the two objects.
Newton extended this law to include all the heavenly bodies such as the moon, the sun and the planets. What about circular motion? It is not ethereal motion, but a form of acceleration, as we have seen. And acceleration requires force. If we tie a stone to a string and twirl it around, the stone will fly in a circular path because the tension in the string provides the force that generates the acceleration (equal to v2/r where v is the speed of the stone and r the length of the string). In the case of a planet circling the sun, the force comes from gravity. Using Kepler’s data of planetary motion Newton inferred that the further a planet is from the sun, the smaller is its acceleration, and that this acceleration is inversely proportional to the