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Question 1: In cylindrical coordinates (ds)2 = (dΡ)2 + p2(dΦ)2+ (dz)2. Find the non-zero Christoffel symbols and the equations, of the geodesic, for the two dimensional case of move-ment on the surface of a cylinder of radius Ρ = R.
Question 2: The motion of an object of mass m in two dimensions, in the presence of a gravita¬tional field may be determined from the Lagrangian
L = 1/2m (x2 + y2) - mgy
Consider the transformation given by
x' = x + α ± βt
y' = y
where α and β are constants. For this system
(a) Show that the transformation is an invariance transformation by finding the function A.
(b) Find the related infinitesimal invariance transformation and calculate SA.
(c) Find the associated constants of the motion for the two parameter transformation above.
A luge and its rider, with a total mass of 104 kg, emerges from a downhill track onto a horizontal straight track with the initial speed of 53 m/s. suppose they stop with the constant deceleration of 2.30 m/s2.
Two long, parallel conductors carry currents I1 = 3.10 A and I2 = 5.10 A, both directed into the plane of the computer screen. Find out the magnitude and direction of the resultant magnetic field at a point midway between the wires. (b) Find out the ..
What is the wavelength of the waves emitted by source? What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling straight toward the ship at 4.95 ? Assume that the ship is at rest in the..
A pair of speakers separated by 0.700m is driven by the same oscillator at a frequency of 662Hz. An observer, originally positioned at one of the speakers, begins to walk along a line perpendicular to line joining the speakers. (Assume the speed o..
A railroad car with a mass of 2 x10^4 kg moving at 3.0 m/s collides and joins with 2 railroad cars already joined together, each with the same mass as the single car and initially moving in the same direction at 1.20 m/s.
Find an equation for the change in wavelength of a scattered photon by Compton effect.
A simple harmonic oscillator consists of a block of mass 2.2kg attached to a spring of spring constant 26N/m. When t = 1.60 s, the position and velocity of the block are x = 0.128m and v = 3.170 m/s. (a) What is the amplitude of the oscillations? ..
An explosive charge imparts a velocity of 10,350 feet per second to a mortar as it exits the muzzle of mortar. If the mortar is elevated at 80 degrees what are the horizontal and vertical velocities on the mortar shell.
A ball has fallen to the street below, and a passerby returns it by launching it at an angle of 53.0° above the horizontal at a point 26.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall.
A 3000 pound car crashes into a concrete jersey barrier moving 3 sections (totaling 12,000 pounds) laterally 24 inches. How fast was the car going on impact.
What are the components of the ships displacement
How many electrons are there in a tablespoon. Find the tension in each cable. right cable and left cable.
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