A 8 kg block of ice, released from rest at the top of a 1.5 m long frictionless ramp, slides downhill, reaching a speed of 2.5 m/s at the bottom. What is the angle between the ramp and the horizontal? What would be the speed of the ice at the bottom if the motion were opposed by a constant friction force of 10 N parallel to the surface of the ramp?

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?