By S.Cahn, B.Nadgorny
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Extra resources for A Guide to Physics Problems. part 12 Mechanics, Relativity, and Electrodynamics
21 Neutron Scattering (Moscow Phys-Tech) Neutrons can easily penetrate thick lead partitions but are absorbed much more efficiently in water or in other materials with high hydrogen content. 21). 22 Collision of Mass–Spring System (MIT) A mass with initial velocity strikes a mass-spring system initially at rest but able to recoil. The spring is massless with spring constant (see Figure P. 22). There is no friction. a) What is the maximum compression of the spring? b) If, long after the collision, both objects travel in the same direction, what are the final velocities and of and respectively?
31 MECHANICS a) Write the Lagrangian and the Hamiltonian, and rewrite them in terms of the variables b) Find an integral of motion other than the energy, and show that its Poisson bracket with is zero. 51 Particle in Magnetic Field (Stony Brook) a) Give a relationship between Hamilton’s equations under a canonical transformation. Verify that the transformation is canonical. 52 introduced above, using Adiabatic Invariants (Boston (a)) and Dissolving Spring (Princeton, MIT (b)) a) (Adiabatic Invariants) Consider a system with canonical variables At the time and let be an arbitrary closed path in phase space 32 PROBLEMS Assume that the point moves in phase space according to of Hamilton's equations.
2b). a) In the Earth frame, how much time will pass before the rockets collide? b) How fast is rocket B approaching in A’s frame? How fast is rocket A approaching in B’s frame? c) How much time will elapse in A’s frame from the time rocket A passes point until collision? How much time will elapse in B’s frame from the time rocket B passes point until collision? 3 Photon Box (Stony Brook) An empty box of total mass M with perfectly reflecting walls is at rest in the lab frame. 3). RELATIVITY 35 a) State what the rest mass of the system (box + photons) will be when the photons are present.
A Guide to Physics Problems. part 12 Mechanics, Relativity, and Electrodynamics by S.Cahn, B.Nadgorny