A copper wire of length L and cross-sectional area A has resistance R. A second copper wire at the same temperature has a length of 2L and a cross-sectional area of (1/2)A. What is the resistance of the second copper wire?

Light traveling in a medium with a refractive index 1.19 is incident on a plate of another medium with index of refraction 1.79. at what angle of incidence is the reflected light fully polarized?

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.

In addition to gravity, what is the other predominant force that affects the motion of a pendulum?