A block is released from A on a frictionless track as shown in Fig. 7.2.6. What is the magnitude of radial acceleration and the total acceleration of the block at B ?

A block is released from A on a frictionless track as shown in Fig. 7.

1.	A block is released from A on a frictionless track as shown in Fig. 7.2.6. What is the magnitude of radial acceleration and the total acceleration of the block at B ?
Answer» Solution :Let AC = H= 7 m, Radius of the curved portion = r = 3 m Decrease in P.E. of the block in REACHING B = Increase in its K.E. `mg(H-r) = 1/2 MV^(2)` `v^(2) = g(H-r)` Radial acceleration `=v^(2)/r = (g(H-r))/r` `a_(r) = (9.8 (7-3))/3 = 13.1 m//s^(2)` TANGENTIAL acceleration `=a_(t) = 9.8 m//s^(2)` Total acceleration =a= ? `a= sqrt(a_(r)^(2) + a_(t)^(2))` `=sqrt(13.1^(2) + 9.8^(2))` `=16.36 m//s^(2)`