BSC PHYSICS Study Guide - Virtual Displacement, Net Force, Virtual Work

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prasadkizhakepatt

25 Jun 2022

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University of Calicut

Department

Physics

Course

BSC PHYSICS

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The guideline shows that any arrangement of powers is in balance assuming the applied powers are added to imaginary powers. The amount of the differences between the powers applied on an arrangement of particles (with non-zero rest mass) and the time subordinates of the momenta of the framework is zero when the framework is projected into virtual removal. " D"alembert"s principle is one more understanding of newton"s regulation however the previous is a more summed up rendition as it changes an issue in energy to statics. It is utilized in tackling issues in statics, a part of mechanics those examinations frameworks that have no speed increase and are in harmony as for their current circumstance. And furthermore is utilized to manage issues in elements, predictable with requirement powers. The mathematical representation of the principle is done using newton"s dot notation. Thus in general form that is in a system of particles with variable mass, it is written as:

Related Questions

You see two carts connected by a spring and oscillating on ahorizontal air track. You happen to know that the spring constantof the spring is k=50.0 N/m. You use Newton's second law todetermine that the period of oscillation is the same for each cartand is related to the masses of the carts by

T = 2pi ( squareroot ((m_1m_2)/(k(m_1+m_2)))).

Using a position vector, you determine that the positions of thecarts as functions of time can be expressed as
x_1(t) = 2.70[1 - cos(18.0t)] and
x_2(t) = 10.70 +1.29cos(18.0t)
wher the coordinates are in centimeters and the time is inseconds.
a) Use the principle of conservation of momentum to find the massesof the carts.
b) Generate a table of the values of x_1, x_2 for every 1 s fromt=0 to t=35 s.
For each of these times, also calculate the position of the centerof mass, the total momentum of the two-cart system, and the forceof the spring on each cart.
Verify that the center of mass does not move, that the totalmomentum is conserved, and that the forces on the carts from thespring have the same magnitude but in opposite directions.
c) Use the table to find the equilibrium length of the spring.

a) Use the principle of conservation of momentum to find the massesof the carts.

b) Generate a table of the values of x₁,x₂ for every 1 s from t = 0 to t = 35 s.
For each of these times, also calculate the position of the centerof mass, the total momentum of the two-cart system, and the forceof the spring on each cart.
Verify that the center of mass does not move, that the totalmomentum is conserved, and that the forces on the carts from thespring have the same magnitude but in opposite directions.

c) Use the table to find the equilibrium length of thespring.

Pierre de Fermat (1601–1665) showed that whenever light travels from one point to another, its actual path is the path that requires the smallest time interval. This statement is known as Fermat’s principle. The simplest example is for light propagating in a homogeneous medium. It moves in a straight line because a straight line is the shortest distance between two points. Derive Snell’s law of refraction from Fermat’s principle. Proceed as follows. In Figure P35.74, a light ray travels from point P in medium 1 to point Q in medium 2. The two points are, respectively, at perpendicular distances a and b from the interface. The displacement from P to Q has the component d parallel to the interface, and we let x represent the coordinate of the point where the ray enters the second medium. Let t 5 0 be the instant the light starts from P.

(a) Show that the time at which the light arrives at Q is

(b) To obtain the value of x for which t has its minimum value, differentiate x with respect to t and set the derivative equal to zero. Show that the result implies

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BSC PHYSICS Study Guide - Virtual Displacement, Net Force, Virtual Work

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Physics: Principles with Applications

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