Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Classical Dynamics of Particles and Systems
9.21P9.22P9.23P9.24P9.25P9.26P9.27P9.28P9.29P9.30P9.31P9.32P9.33P9.34P9.35PIn an elastic collision of two particles with masses m1 and m2, the initial velocities are u1 and u2 = u1. If the initial kinetic energies of the two particles are equal, find the conditions on u1/u2 and m1/m2 such that m1 is at rest after the collision. Examine both cases for the sign of .9.37P9.38P9.39P9.40P9.41P9.42P9.43P9.44P9.45P9.46P9.47P9.48P9.49P9.50P9.51P9.52P9.53P9.54P9.55P9.56P9.57P9.58P9.59P9.60P9.61P9.62P9.63P9.64P9.65P9.66P9.67P10.1P10.2P10.3P10.4P10.5P10.6P10.7P10.8P10.9P10.10P10.11P10.12P10.13P10.14P10.15P10.16P10.17P10.18P10.19PCalculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?10.21P10.22P11.1P11.2P11.3P11.4P11.5P11.6P11.7P11.8P11.9P11.10P11.11P11.12P11.13P11.14P11.15P11.16P11.17P11.18P11.19PA uniform rod of length b stands vertically upright on a rough floor and then tips over. What is the rods angular velocity when it hits the floor?11.21P11.22P11.23P11.24P11.25P11.26P11.27P11.28P11.29P11.30P11.31P11.32P11.33P11.34P12.1P12.2P12.3PRefer to the problem of the two coupled oscillators discussed in Section 12.2. Show that the total energy of the system is constant. (Calculate the kinetic energy of each of the particles and the potential energy stored in each of the three springs, and sum the results.) Notice that the kinetic and potential energy terms that have 12 as a coefficient depend on C1 and 2 but not on C2 or 2. Why is such a result to be expected?12.5PTwo identical harmonic oscillators are placed such that the two masses slide against one another, as in Figure 12-A. The frictional force provides a coupling of the motions proportional to the instantaneous relative velocity. Discuss the coupled oscillations of the system.12.7P12.8P12.9P12.10P12.11P12.12P12.13P12.14P12.15P12.16P12.17P12.18P12.19P12.20P12.21P12.22P12.23P12.24P12.25P12.26P12.27P12.28P13.1P13.2P13.3P13.4P13.5P13.6P13.7P13.8P13.9P13.10P13.11P13.12P13.13P13.14P13.15P13.16P13.17P13.18P13.19P13.20P13.21P13.22P14.1P14.2PShow that the equation
is invariant under a Lorentz transformation but not under a Galilean transformation. (This is the wave equation that describes the propagation of light waves in free space.)
14.4P14.5P14.6P14.7P14.8P14.9P14.10P14.11P14.12P14.13P14.14P14.15P14.16P14.17P14.18P14.19P14.20P14.21P14.22P14.23P14.24P14.25P14.26P14.27P14.28P14.29P14.30P14.31P14.32P14.33P14.34P14.35P14.36P14.37P14.38P14.39P14.40P14.41P14.42P