Una barra de 5 metros de longitud y 240 N de peso descansa sobre dos apoyos situados tal como muestra la figura. Calcula la fuerza de reacción que ejerce cada apoyo sobre la barra.

"if the pressure acting on an ideal gas at constant temperature is tripled, its volume isa) reduced to one-third.b) increased by a factor of three.c) increased by a factor of two.d) reduced to one-half"

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.

Eof 20 degrees. the index of refraction of air is 1.0003, and the index of refraction of water is 1.33. the angle of refraction rounded to the nearest whole number is °.