What is the tension in the string when ball reaches Q?
You might think the tension in the string should be “mg”, but that is not correct. The tension depends not only on the weight of the ball, but also how fast the ball is moving in a circle. You can think of it as though the “centrifugal force” of the circular motion is adding to the tension. To analyze it more precisely: At point Q, the ball is moving at a certain speed “v” (we’ll figure out “v” later). Whenever something moves in a circular path, it has a centripetal acceleration “a_c” given by: a_c = v²/R (“R” is the radius of the circle; which in this case is just the length of the string). The direction of the centripetal acceleration is always toward the center of the circle (which in this case, is straight up). So, at point Q, the ball’s vertical accelaration is: a_vert = a_c = v²/R But Newton’s 2nd law says that the net vertical force (Fnet_vert) is: Fnet_vert = m(a_vert) so: Fnet_vert = mv²/R Furthermore, the net vertical force is the combination of all the vertical forces. Ther
