a small block slides from rest from the top of a frictionless sphere of radius R, how far below the top x does it lose contact with the sphere? the sphere doesnt move. the question is from kleppner's in troduction to mechanics page 196 problem 4.6. (my scanner doesnt work so i cant scan the picture). anyway, x is the displacement from when the block was on top the shpere up until where it loses contact with the sphere. what i got so far is: i calculated the tan of the angle of velocity, i got that tan(a)=sqrt(2Rx-x^2)/x and i got by energies that v^2=2xg and i know that v_y/v_x=tg(a) and v^2=v_y^2+v_x^2 and that v_y^2=xg, but after all that i didnt get the answer in the book, which is R/3. can someone help me here? thanks in advance.