Aproton is confined in a uranium nucleus of radius 7.2x10-15 m. determine the proton’s minimum kinetic energy according to the uncertainty principle if the proton is confined to a 1 dimensional box that has the length of the nuclear diameter. you can assume that the velocities involve are non-relativistic, so that ekin=p2 /(2m).

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.