Answered: 4. The Lagrangian of a relativistic… | bartleby

Related questions

Question

4.
The Lagrangian of a relativistic particle is given by
v2
L = -moc² 1-
where mo is the rest mass of the particle, v is its velocity, and V is not velocity
dependent. Find the generalized momentum and the Hamiltonian H. It may be shown
that the relativistic kinetic energy T is -moc² (1-2) - V. Check that H = T + V.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Needs Complete typed solution with 100 % accuracy.
I Review I Constants I Periodic Table The position of a 55 g oscillating mass is given by T (t) = (1.7 cm) cos 13t, where t is in Part C seconds. Determine the spring constant. Express your answer in newtons per meter. Hνα ΑΣφ ? k = N/m Submit Request Answer Part D Determine the maximum speed. Express your answer in meters per second. Iνα ΑΣφ Umax = m/s Submit Request Answer
that the axes get closer to one another. 2. Prove that the "interval", defined as x² +v² + =² – c²¢ is a conserved quantity across reference frame transformations. 3. Consider two events. Give an example of coordinates x,y,z,t and x',y',z',t and relative
An asteroid of mass 1000 kg travels through space with speed a) What is the total energy of the asteroid? (You can leave your response as a math function, but please simplify as much as you can.) b) The asteroid has a rest length of 20 m. What length would an observer on Earth see? (You can leave your response as a math function, but please simplify as much as you can.)
Consider the equation for kinetic energy: KE = 1/2mv^2 = 1/2 * m * v^2. If I ask you to take the derivative of kinetic energy, you should ask "the derivative with respect to what?" a) Suppose mass m is constant. Compute the derivative of KE with respect to v, (d(KE)/dv). b) Who takes derivatives with respect to velocity? No one. Except you, just now. Sorry. The rate of change of energy with respect to time is more important: it is the Power. Now, consider velocity v to be a function of time, v(t). We will rewrite KE showing this time dependance: KE= 1/2 * m * v(t)^2. Show that (d(KE)/dt) = F(t)v(t). Hint: use Newton's second law, F = ma, to simplify. c) In the computation above, we assumed m was constant, and v was changing in time. Think of a physical situation in which both m and v are varying in time. d) Compute the Power when both mass and velocity are changing in time. (First rewrite KE(t) showing time dependence, then compute (d(KE)/dt).
2. An alternative derivation of the mass-energy formula E, = moc² also given by Einstein, is based on the principle that the location of the center of mass (CM) of an isolated system cannot be changed by any process that occurs inside the system. The Figure below shows a rigid box of length L that rests on a frictionless surface; the mass M of the box is equally divided between its two ends. A burst of electromagnetic radiation of energy E, is emitted by one end of the box. According to classical physics, the radiation has the momentum p = "0%c , and when it is emitted, the box recoils with the speed v z Eo/ so that the total momentum of Mc the system remains zero. After a time t z L/c the radiation reaches the other end of the box and is absorbed there, which brings the box to a stop after having moved the distance S. If the CM of the box is to remain in its original place, the radiation must have transferred mass from one end to the other. Show that this amount of mass is m, = c2.
Please please please answer as fast as possible please
Suppose an alpha particle (which has a mass of 6.645 × 10-27 kg) is moving at 0.29c.Randomized Variablesv = 0.29 c Part A) What is the momentum of the alpha particle in kg ⋅ m/s?