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 ?

Explanation

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)`