物理代写 physics代写 Physical Constants代写

2022/01/10天文学代写物理代写 Physical Constants代写 physics代写物理代写相对论代写673

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物理代写 Answer two questions. If you answer more than two questions, credit will only be given for the best two answers. 1.In this question you should take the

Answer two questions. If you answer more than two questions, credit will only be given for the best two answers.

1.

In this question you should take the mass of the proton to be 938 MeV/c² and the mass of the neutral pion to be 135 MeV/c².

(a) Our galaxy is about 105 light-years across. The highest energy cosmic rays observed to date are protons with energy of about 1020 eV. Estimate the time taken for a proton with this energy to cross the galaxy, as measured in:

i. the rest frame of the galaxy;

ii. the rest frame of the proton.

(b) Cosmic ray protons may lose energy through collisions with cosmic microwave background photons through the reaction

p + γ → p + π⁰ .

Estimate the threshold proton energy required for this reaction to take place ‘head-on’ with a photon whose energy corresponds to the characteristic cosmic microwave background temperature of 2.7 K.

(d) Consider three objects, A, B and C. As observed in the laboratory frame of reference, B is at rest, while A and C approach B from the same direction along a common axis, with A more distant than C and A moving at speed v. How fast must C be moving in the laboratory frame if an observer in C’s rest frame sees A and B approaching from opposite directions at the same speed?

2. 物理代写

A thin rod of length L and mass M has a mass per unit length that varies as

where x is the distance along the rod and ρ₀ is a constant. The rod hangs under gravity, pivoted at its lighter end (x = 0).

(a) Find the distance between the pivot and the centre of mass of the rod.

(b) Find the moment of inertia of the rod about an axis perpendicular to the rod at the lighter end of the rod. Express your answer in terms of M and L.

(c) Hence find the moment of inertia of the rod about an axis perpendicular to the rod at the centre of mass, in terms of M and L.

(d) Show that if the rod is displaced slightly from the vertical and released, it executes simple harmonic motion in the angle of the displacement and find an expression for the time taken per oscillation.

(e) Find the distance between the pivot and the centre of percussion of the rod when it hangs under gravity.

(f) What would be the time period of oscillations if the rod were replaced by a simple pendulum of the same mass, with all of the mass located at the centre of percussion?

3. 物理代写

A particle of mass m slides on a frictionless table. The particle is attached to one end of a light spring, with the other end of the spring attached to a fixed pivot. The spring produces a force of magnitude kr on the particle where r is the distance between the pivot and the particle. The particle initially moves in a circle and the system has a total energy E₀.

(a) Find expressions for the radius r0 of the circular orbit and the velocity v0 of the particle in the circular orbit in terms of any of E0, m and k.

(b) The effective potential energy of an orbiting particle of mass m in a central conservative potential V (r) is

where r is the particle’s distance from the origin and l is its angular momentum about the origin. Derive an expression for the effective potential for the mass on the spring in terms of any of the variables k, m, E₀ and r. Sketch the effective potential as a function of r, indicating the position of the circular orbit.

(c) While it is moving in a circle as described above, the particle is struck by a sudden sharp blow giving it an instantaneous velocity boost, ∆v, inwards towards the pivot. Find an expression for the new total energy of the system, E_tot, in terms of any of E₀, k, m and ∆v. Sketch the trajectory of the particle before and after the velocity boost on a single diagram.

(d) Find expressions for the maximum and minimum values of r for the new orbit as a function of any of the variables k, m, E₀ and E_tot.

Physical Constants and Units