Will the kinetic and/or potential energy contain an explicit time dependence for scleronomic constraints? How about for rheonomic constraints? Explain
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Will the kinetic and/or potential energy contain an explicit time dependence for scleronomic constraints? How about for rheonomic constraints? Explain
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- The difference of the scalar potential squared and the modulus of the vector potential squared, Φ2 - |A|2, is Lorentz invariant (a Lorentz scalar). why the statement true?Please explain in detail An observer P stands on a train station platform as a high-speed train passes by at u/c = 0.8. The observer P, who measures the platform to be 60 m long, notices that the front and back ends of the train line up exactly with the ends of the platform at the same time. (a) How long does it take the train to pass P as he stands on the platform, as measured by his watch? (b) According to a rider T on the train, how long is the train? (c) According to a rider T on the train, what is the length of the train station platform?Problem 2 The relativistic Lagrangian for a particle of rest mass m moving along the x-axis in a potential V(x) is given by 2 L = -mc² 1 V(x) c2 (a) Derive the Euler-Lagrange equation of motion. (b) Show that it reduces to Newton's equation in the limit |*| << c. (c) Compute the Hamiltonian H of the system. Eliminate ȧ from the Hamiltonian by using the equation ƏL p = ax and write H = H(p, x) as a function of x and p only.
- A free neutron has a mean lifetime of 15 minutes when at rest. How fast must it moves to have a mean lifetime of 60 minutes?i) Contrast the processes of induced and spontaneous emission. We need to know the meaning of Einstein's coefficients. ii) What is the frequency difference between the 20th and 21st resonant longitudinal modes if the cavity length is 20 cm?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?