Problem 6-23 Centripetal force - A

A child has tied a piece of wood of mass \(0.47\; kg\) to a string and is swinging it in a vertical circle of radius \(83\; cm\). At the top of the circle:

(a) draw a free body diagram for the wood,
(b) determine the magnitude of the tension in the string, if the speed of the wood is \(3.7 \;m/s\).

Accumulated Solution

FBD with forces and directions indicated


Both the weight and the tension in the string act toward the centre when the block is in this position (Note that this is not the case anywhere else. For example, at the bottom of the circle the tension is still toward the centre (up), but the weight acts down.)

The correct form of Newton's second law in this case is:

(A)   \(mg + T = m(v^2/r)\)

(B)   \(mg - T = m(v^2/r)\)

(C)   \(T - mg = m(v^2/r)\)