Statics: Centre of Mass

Centre of mass and motion

This demonstration shows that a body can appear to move up a slope unaided.

(a)                                                                      (b)
Fig. 2-10: Centre of mass and motion

Take two support rails which incline in both the vertical and horizontal planes as shown in Fig. 2-10. When a doubly conical solid body is placed on the lower ends of the rails, it can be observed that the body rotates and travels up to the higher end of the rails (Fig. 2-10b).

It appears that the body moves against gravity though in fact it moves with gravity. When the locations of the centre of mass of the body, C, are measured at the lowest and highest ends of the rails, it is found that the centre of mass of the body at the lower end is actually higher than that when the body is at the highest end of the rails. It is thus gravity that makes the body rotate and appear to move up the slope.

The reason for this lies in the design parameters of the rail supports and the conical body. The control condition is that the slope of the conical solid body should be larger than the ratio of the increased height to a half of the increased width of the rails between the two ends.