Askateboarder wants to cross a large playground and notices that there are large shapes painted on its asphalt surface. one shape is a large circle that covers the entire playground. inscribed in that circle is a square, with one point at the skateboarder’s feet and the other at his destination. the surface is rough and, therefore, friction is present. what path does he follow in order to minimize the work done by nonconservative forces?

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?