A small block of mass m is released from rest at a height h above the lowest point of a smooth vertical loop–the–loop track of radius R. The block moves along the track and passes over the topmost point of the loop.
a. (i) Write the mechanical condition that must be satisfied at the highest point of the loop for the block to remain in continuous contact with the track.
b. (ii) Obtain an expression for the minimum speed that the block must possess at the bottom of the loop so that the condition in part (i) is just met.
c. (iii) Hence derive the least height hmin (measured from the bottom of the loop) from which the block should be released to complete the loop without losing contact.