Anucleus of helium with mass 5 u breaks up from rest into a nucleus of ordinary helium (mass = 4 u) plus a neutron (mass = 1 u). the rest energy liberated in the break-up is 0.89 mev, which is shared (not equally) by the products. (a) using energy and momentum conservation, find the kinetic energy of the neutron. (b) the lifetime of the original nucleus is 1.0 × 10−21 s. what range of values of the neutron kinetic energy might we measure in the laboratory as a result of the uncertainty relationship?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.