Question

A sphere of mass M and radius R starts at rest and rolls without slipping down an incline and embeds itself in a hollow cube at the bottom that is only 1/5 its mass. If the incline is h tall and the table has a height of D from the floor, at what horizontal distance from the table do the two objects land? The cube/sphere combination leaves the incline moving horizontally.

Answer 1

E Ell mass of sphere M, = M " " Cube Ma = Total Kinetic energy of sphere is Ex = £mu²+ £ I w² amute mu) (Ž)* = 2 mut & mu? . - Za mo? using energy conservation. 1/2 muz nigh v logh = v= lotta Now for collision of sphere with cube using conservation of linear momentum MV+ 4 x 6 = (M +v x rogh = AMV = v'z Eliogh - Now for the motion of system .. down the table, using vertical ě a motion, h= Uyt that D=0+ adopttale using horizontal motion, x= v't = 8 logh * = o p logh Ka D = . The