INTRODUCTION. Newton developed this law of motion has significant mathematical and physical elucidation that are needed to understand the motion of objects in our universe. Newton introduced the three laws in his book Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy), which is generally referred to as the Principia. He also introduced his theory of universal gravitation, thus laying down the entire foundation of classical mechanics in one volume in 1687. These laws define the motion changes, specifically the way in which those changes in motion are related to force and mass.
Galileo’s Gravitational Experiment D. G. Lacsamana De La Salle University 2401 Taft Avenue, Manila, Philippines Abstract: The experiment is entitled the gravitational experiment as what Galileo discovered during his time. The purpose of this was to prove that the acceleration at free-fall of an object is the same as the acceleration of an object sliding down in an inclined surface. The procedure involved changing of different angles of the inclined plane holding the mass of the cart and the distance travelled constant considering the average time with 10 trials. The results showed that the acceleration was directly proportional to the angle. Introduction During the 17th century, a lot of studies are being conducted to study motion.
Newton developed this law of motion has significant mathematical and physical elucidation that are needed to understand the motion of objects in our universe. Newton introduced the three laws in his book Philosophiae naturalis principia mathematica (Mathematical Principles of Natural Philosophy), which is generally referred to as the Principia. He also introduced his theory of universal gravitation, thus laying down the entire foundation of classical mechanics in one volume in 1687. These laws define the motion changes, specifically the way in which those changes in motion are related to force and mass. There are three laws of motion which were introduced by Sir Isaac Newton which are Newton’s First Law , Newton’s Second Law and Newton’s
CHAPTER 3 – Theoretical and Numerical Computational Solution of the Schrodinger Equation 3.1 Theoretical Solution The theoretical solution of the time independent and the time dependent Schrodinger equation is analysed. Solution to Time Dependent Schrodinger Equation: method of separation of variables  TDSE: EΨ(t,x)= (〖-ħ〗^2/2m d^2/(dx^2 ) + U(x))Ψ(t,x)-→ EΨ(t,x) = ĤΨ The potential energy in the Hamiltonian is time independent: U = U(x). Assuming: Ψ(t,x) = Ψ(x)f(t) So TDSE is re-written as: iħΨ(x) df(t)/dt = 〖-ħ〗^2/2m (d^2 Ψ(x))/(dx^2 ) f(t)+ UΨ(x)f(t) Multiply through by (1/Ψ(x)f(t)) to make the R.H.S exclusively t-dependent and the L.H.S exclusively x-dependent TDSE is re-written as: iħ 1/(f(t))
The relationship of tangential velocity and the mass of the object will be observed and determined. Tangential velocity is an object’s speed along a circular path. The uncertainty is the numerical value of ranges of the result. There are three measuring instruments which require uncertainty. The weighing scale and the stop watch are digital devices and their uncertainties are the same as the smallest division.
To define the displacement of the mass as a function of time, u(t), subject to the initial conditions of the system. One approach to solving this partial differential equation is to assume a solution of the form: Take the second derivative with respect to time of: Substitute the given equation: which can be simplify as: Solving for r makes two possible root of an imaginary number: Where i = √(-1) following the solution given: Defining the radical term in the exponent to be the circular natural frequency of vibration of the system: Circular frequency is related to the natural frequency by: Obataining the natural period by: Evaluating the coefficent in the given equation, we neet to determine the two initial condition. This causes initial displacement and velocity mass: Substituting these equation and its first derivative we attain this equation: Damped Free Vibration As shown in the figure single-degree-of-freedom (SDOF) system has both a spring and dashpot If we inspect a free-body diagram of the mass we see that an supplementary force is delivered by the dashpot. The force is proportional to the velocity of the
Work of Heisenberg was further developed by Born and Jordan, which was a birth of matrix mechanics. Soon after emergence of a Schrodinger’s equation, equivalence of these two forms was proven. Final formation of a quantum mechanics as a theory is due to work of Heisenberg of 1927 in which the principle, claiming that any physical system cannot be in a state where coordinates of its center of mass and an impulse are precise values at the same time, was formulated. This is now called "Heisenberg’s uncertainty principle". The indeterminacy relation establishes that concepts of coordinate and an impulse in the classical sense cannot be applied to microscopic objects.
In this essay, I am going to describe and explain the basic principles in string theory. String theory is a theoretical framework in which particles are replaced by strings. The strings are like ordinary particles with mass, charge but other properties are determined by the vibrational state of the string and they are only in one dimension. String theory originated from the Kaluza-Klein theory in 1921. In 1970 the official string theory is formulated.
Motion is the change in position over time against a reference point, and is the procedure of an object changing place or position. Sir Isaac Newton, a famous mathematician and scientist, had created three laws based on motion. The first law was based on inertia, the tendency of an object to resist any change in motion, which states, “Objects at rest, stay at rest, unless acted upon by a force,” and, “Objects in motion, stay in motion, unless acted upon by a force.” This law explains that if an object were to travel at a constant speed in the same direction, it would continue to do this until it is pulled or pushed by something. If we think about a gravity-free zone, such as space, we could picture throwing a rock out into outer space. And this marble would continue to go at the same speed in the same direction unless there is a force, a push or pull, acting upon by it, making it either slow down, speed up, or just change it’s direction.
Upon the removal of the load or force, an object would return to its original size and shape. Mathematically, this can be expressed as F=kx, where F is the deforming force, x is the size of the deformation, and k is the spring constant. In this experiment, the spring constant of the plunger can be determined by applying force on the spring and recording the displacement of the spring plunger. When the force is plotted versus displacement, the slope of the resulting straight line is equal to the spring constant, k. To get the spring potential energy, the formula PEspring = ½ kx2. 2.