Physics and Mechanical Universe
The mechanical universe
Performed by the California Institute of Technology The Corporation for Community College. It takes a tour of the different fields of physics: electricity, magnetism, mechanics, etc.
Lesson 1, Introduction to the mechanical universe.
The investigation begins with the formulation of some questions. This prolegomena introduces us to an Aristotelian world in conflict. It presents the ideas and people that revolutionized scientific thinking from Copernicus, through Newton, to the present day; and links the Celestial Physics with the Physics on Earth. Pedagogical objectives: define the units of length, time and mass; know the units of the “SI” and some units of “Ss. Angloamericanos”; interpret the conversion factors and use them to move from one system of units to another; express large and small numbers in scientific notation; know the usual scientific abbreviations of the units.
Lesson 2, The law of the fall of bodies.
With the conventional knowledge provided by the Aristotelian vision of the world, one could see that heavy bodies fall faster than light ones. Galileo deduced that the distance that a body has traveled in its fall is proportional to the square of the time taken. With the mathematical tool called derivative we deduce the concepts of speed and acceleration. Pedagogical objectives: Define average speed, average acceleration, speed and acceleration. Identify that the distance a body travels when falling into a vacuum is proportional to the square of time used. Recognize that all bodies fall into a vacuum with the same constant acceleration. Analyze the significant aspects of the historical environment that led to the discovery of the “Law of the fall of bodies.” Use algebraic expressions to solve problems that describe the movement of bodies in free fall. Interpret the derivative as a limit or instantaneous rate of change.
Lesson 3, Derivatives.
The role of mathematics in the physical sciences. As a theoretical concept and practical tool, the derivative helps determine the instantaneous velocity and acceleration of a falling body. Differentiation develops further to calculate how any one quantity changes in relation to another. The power rule, the product rule, the chain rule: with a few simple rules, differentiating any function is an easy task. Pedagogical objectives: Define the concept of derivative. Interpret the relationship between tangent and derivative. Calculate elementary derivatives using differentiation rules.
Lesson 4, Inertia.
Rise and fall of Galileo. Copernicus showed that the Earth rotates on its axis and describes an orbit around the sun. Considering its implications, it was a rather dangerous assumption, in those times, which provoked such adventurous questions as: Why do objects fall to Earth instead of erring in space? And in this heretical scheme of things in which the Earth was not the center, where was God? Risking more than his privileged status in Rome, Galileo contributed to answering such questions with the formulation of the “Law of inertia.” Pedagogical objectives: Interpret the “Law of inertia.” Distinguish between the Aristotelian and Galilean description of the movement. Recognize that the description of a movement is not the same when it is analyzed from different reference systems. Indicate that the parabolic paths are the result of the composition of a constant speed in the horizontal direction and a constant vertical acceleration. Appreciate the historical significance and universality of the “Law of inertia” of Galileo.
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Lesson 5, Vectors.
Physics must explain not only “why and how much,” but also “where and how.” Physicists and mathematicians designed a way to describe the quantities that have an address, a meaning and a module. Laws dealing with phenomena of distances and velocities are universal laws. And when describing quantities such as displacement and velocity, a law of Physics is universally expressed in a way that is the same for all coordinate systems. Pedagogical objectives: Add and subtract graphically vectors by handling the “parallelogram rule”. Indicate the components of a vector and use them analytically for addition and subtraction. Interpret the scalar product of two vectors. Describe the vector product of two vectors.
Lesson 6a, Newton’s law.
Isaac Newton established the laws for all the phenomena of “The mechanical universe.” As a generalization of the “Galileo Law of inertia,” Newton’s “First Law” states that every body remains at rest or continues in uniform rectilinear motion unless a net resulting force acts on it. His “Second Law”, the deepest affirmation of classical mechanics, relates the causes and changes in the state of motion for all objects in the cosmos. Newton’s “Third Law” explains the phenomenon of interactions: every force-action generates an equal and opposite force-reaction. Pedagogical objectives: Explain the definitions of force and mass and say what Newton’s Law of movement consists of. Distinguish between mass and weight. Know the following units and know how kilogram, newton and dyna are defined. Recognize that forces always occur in pairs, as “action-reaction”, and act on different bodies, and that they can never act as balancing forces of a body. Understand that the degree of application of the “Newton’s second law” emerges from it as a differential equation. Analyze projectile motion as a consequence of Newton’s laws.
Lesson 7a, Integration.
Newton and Leibniz developed the mathematical calculation. And they produced the greatest scientific breakthrough in more than 2000 years from the Greek Golden Age to Europe at the end of the seventeenth century. Newton Leibniz independently concluded that differentiation and integration are inverse processes. His exciting intellectual discovery dramatically reflected the times that were running, ending in a controversial personal confrontation. Pedagogical objectives: Define integration as the process of obtaining the primitive of a derivative. Understand the relationship between integration and measurement of areas. Expose the “Second Fundamental Theorem of Calculation. Apply the” Second elementary Theorem of Calculation “to physical issues.
Lesson 8a, The apple and the moon.
The first consolidated steps towards outer space. In seeking an application to Kepler’s laws, Newton discovered that gravity describes the force between any two particles in the universe. From an English garden to Cape Canaveral and beyond, the “Law of universal gravitation” enunciated by Newton reveals why an apple falls to the ground but the Moon does not. Pedagogical objectives: Recognize that between two objects there is a gravitational force that is directly proportional to the product of the masses and inversely proportional to the square of the distances that separates them. Understand the functional dependence of gravitational force with mass and distance. Use some formulas to solve problems. Recognize that, for sufficiently small speeds, The time it takes for a projectile to fall to Earth is independent of its horizontal velocity, but for high horizontal velocities, the effect of terrestrial curvature must be taken into account. Describe the orbital movement in terms of the “Law of inertia” and the “Law of universal gravitation.”
Lesson 9a, The circle in motion.
The original Platonic ideal, with those derived from vector functions. According to Plato, the stars are celestial bodies that revolve around the Earth in absolute perfection, describing perfect circles at uniform speed. Even in this imperfect world, the uniform circular motion has a perfect mathematical sense. Pedagogical objectives: Interpret the measures in the uniform circular movement. Describe the relationships between radius, velocity and acceleration in uniform circular motion. Use formulas in problem solving. Handle Newton’s Laws to define the dynamics of circular motion and solve problems of objects that move in circular paths.
Lesson 10a, The fundamental forces of nature.
All physical phenomena of Nature are explained by four forces of interaction: two nuclear forces – strong and weak – that act at the level of the atomic nucleus. The fundamental gravitation force is present throughout the Universe. As is the fourth fundamental force, the electromagnetic one, that unites the atoms of all matter. Pedagogical objectives: Identify which fundamental forces are responsible for an outcome. Describe the Cavendish experiment to determine the universal gravitational constant G. Compare and contrast the electromagnetic and gravitational forces. Know that all contact forces come from electromagnetic forces that act in different and complex ways. Apply the “Newton’s Laws” to solve problems of inclined planes and pulleys. Recognize that the static, maximum friction force, and kinetic friction force are proportional to the normal components of the forces, to the surface in question. Apply the “Newton’s Laws” to problems of circular motion.
Lesson 11a, Gravity, electricity and magnetism.
They are forces that act in the setting of Physics. The gravitational force between two masses, the electric force between two charges, and the magnetic force between two poles; They all have basically the same mathematical formulation. Newton’s manuscripts suggested the existence of connections between electricity and magnetism. Through a scientific hunch, Maxwell saw the matter from a totally innovative perspective. Pedagogical objectives: Indicate a connection between electricity and magnetism. State exemplifications and differences between Gravitation and Electromagnetism. Explain how the speed of light is “bounded” by electromagnetic forces.
Lesson 12a, The Millikan Experiment
How does the technique advance? Through painful trials and errors, he shows us a dramatic recreation of the classic Millikan oil drop experiment. Assuming the electric force in a charged droplet and the viscosity, the charge of an isolated electron was measured. Pedagogical objectives: Describe the Millikan experiment to measure the charge of an electron. Solve viscous force problems. Recognize that every charge is a multiple of the elementary charge unit, that of the electron.
Lesson 13, Energy conservation.
The myth of the “energy crisis”. According to one of the main laws of Physics, energy is neither created nor destroyed. Pedagogical objectives: Define the concepts of work, kinetic energy and potential energy. Understand the relationship between work and energy. Solve problems using the “Principle of energy conservation”.
Lesson 14, Potential Energy.
The issue of stability.Potential energy offers the key, and an identical model, to grasp why the globe has worked within the same method since the start of your time. Pedagogical objectives: Calculate the potential energy function associated with a conservative force. Identify the force F (x) from the potential energy function U (x). Locate the equilibrium points and discuss their stability from a graph of the potential energy function U (x). Use the concepts of gravitational potential energy and the “Principle of energy conservation” to solve escape velocity problems.
Lesson 15, Conservation of the moment.
If the Universe, in its mechanics, is a perpetual clock, what will keep its march until the end of time? Taking an example of Descartes, the linear momentum – the mass product by velocity – amount of movement – is always preserved. The “Newton’s Second Law” materializes the concept of conservation of linear momentum. This law provides a compelling principle for analyzing shocks, even at a pool table. Pedagogical objectives: Recognize the conservation of linear momentum as a consequence of the “Newton’s Second Law”. Identify when the linear momentum of a system is preserved. Recognize the connection between kinetic energy and linear momentum. Solve problems with elastic and non-elastic shocks. Interpret the relationship between momentum and average time of action of a force.
Lesson 16, Harmonic movement.
The music and mathematics of nature. The recovery force and inertia of any stable mechanical system causes objects to perform a simple harmonic movement, a phenomenon that is repeated at exact times. Pedagogical objectives: To know the general characteristics of the simple harmonic movement, including the important property that the acceleration is proportional to the displacement, in its direction; but opposite to it. Relate the simple harmonic movement and the circular movement. Solve problems of objects fixed to vertical or horizontal springs. Analyze the conditions in which the movement of the simple pendulum or physical pendulum is simple harmonic, and be able to find the period of the movement.
Lesson 17, Resonance.
PUBLIC Madrid: Arait Multimedia, DL 1992. PHYSICAL DESK 1 cassette: son., Col. ABSTRACT Music and mathematics of nature., Part II. As Galileo observed, the oscillations of a pendulum increase by applying a small force repeatedly in a synchronous manner. When the frequency of force application coincides with the frequency of the system, the oscillations gain amplitude and the phenomenon known as Resonance occurs. The resonance explains why a suspension bridge can fall by blowing a gentle wind, and also how the human voice can break a glass cup. Pedagogical objectives: Define forced oscillations. Explain the resonance and give some examples. Interpret the relationship between resonance and forced oscillatory movement.
Lesson 18, Waves.
The disturbances of the environment in nature. With an easy periodic motion analysis and slightly of genius, Newton extended the mechanics to the propagation of sound.Pedagogical objectives: Differentiate between transverse and longitudinal waves. Interpret the relationships between speed, period, frequency, wavelength and angular frequency referred to a harmonic wave. Recognize the dependence between speed and the length of a wave, in the case of waves that are transmitted by water, superficially or deeply. Analyze why Newton was not satisfied with his calculation of the speed of sound.
Lesson 19, Kinetic Moment.
An old moment with a new twist. The “second law of Kepler” of the movement of the planets, which here is founded on a much more solid principle, supposes a line, from the sun to a planet, that sweeps equal areas in equal times. The angular momentum is a precession of a linear moment: the vector product of the radius vector by the amount of movement. A spinning force creates a pair or moment. When no pair acts on a system, the angular momentum of the system is preserved. Pedagogical objectives: Define torque and angular momentum. Identify the angular momentum of a system and a particle. Interpret the association between the “second law of Kepler” and therefore the “Principle of conservation of angular momentum”.
Lesson 20, Torsion and gyros.
Why doesn’t a spinning lid fall off? When a pair of forces acts on a rotating object, the angular momentum changes, but the object only performs a precession. The object can be a children’s toy, a piece of a navigation system, or the land itself. Pedagogical objectives: Explain why a spinning gyroscope performs a precession. Describe how to make a gyroscope with a very small degree of precession. Interpret how the Earth acts like a gyroscope.