A uniform straight bar AE is at rest inside a hemisphere in the configuration shown in Fig.6, under the assumption that the friction between the bar and the hemisphere is negligible. This configuration is possible as long as the length of the bar remains within a limited range. The center of the hemisphere is on the vertical plane containing the two points A and B. The upper plane BC of the hemisphere is kept horizontal. The directions AD and BD mean the direction of the force acting on the bar (from the hemisphere) at point A and that on the bar at point B respectively. DG is the direction of the force of gravity acting on the bar, where G is the center of gravity of the bar. The [tex3]\Theta [/tex3]
(=ABC) means the angle between the bar and the horizontal line, and [tex3]\alpha [/tex3]
=ABD, [tex3]\beta [/tex3]
=BAD
- Sem título.png (17.14 KiB) Exibido 1190 vezes
(1)Find the relation between [tex3]\alpha [/tex3]
and [tex3]\Theta [/tex3]
(2)Find the relation between [tex3]\beta [/tex3]
and [tex3]\Theta [/tex3]
(3)Is the case [tex3]\Theta = \pi [/tex3]
/4 possible or impossible?
(4)Is the case [tex3]\Theta [/tex3]
=5 [tex3]\pi [/tex3]
/24 possible or impossible?
(5)In the case [tex3]\Theta = \pi [/tex3]
/6, what is the ratio of the length of the bar to the diameter of the hemisphere?
