Vertical circular motion tension difference · CAP 2005 #12
Physics · mechanics
Problem
A ball of mass m attached to an inextensible string of length R is swung around a vertical circle just fast enough so that the string is always fully stretched. Let ΔT denote the difference between the tension in the string at the bottom and at the top of the circle, vb and vt the speed of the ball at the bottom and at the top, respectively. Then, taking "dependence" to be with respect to a set of independent variables,
(a) ΔT is independent of R, vb and vt;
(b) ΔT is independent of R, but depends on vb2−vt2;
(c) ΔT depends on R, but on neither vb nor vt;
(d) ΔT depends on R and vb2−vt2.