The centripetal force on an object in circular motion is a. perpendicular to the plane of the object’s motion. b. in the plane of the object’s motion and perpendicular to the tangential speed. c. in the plane of the object’s motion and in the same direction as the tangential speed. d. in the plane of the object’s motion and in the direction opposite the tangential speed.

Aparticle of mass m is placed in a one-dimensional box of length l. the box is so small that the particle’s motion is relativistic, so that e p2/2m is not valid. (a) derive an expression for the energy levels of the particle using the relativistic energy–momentum relation and the quantization of momentum that derives from connement. (b) if the particle is an electron in a box of length l 1.00 1012 m, nd its lowest possible kinetic energy. by what percent is the nonrelativistic formula for the energy in error?