- #1
andrien
- 1,024
- 33
A perfectly rough rod is gently placed with one end
upon another rod of equal mass and in the same vertical
plane, moving with the velocity √2gc on a smooth table. If
the initial inclination of the first rod to the horizon be α, and
its length 2a, shew that it will just rise to a vertical position
if
2a (1 -sin α) (5 + 3 cos ^2 α) = 3c sin ^2 a.
i have used the fact that moment of momentum just after putting rough rod will be zero about point of contact to determine initial angular velocity.after that I used equation of energy and conservation of momentum in horizontal direction for the system.but i am not sure about the end condition, i used that reaction will become zero in vertical position and also may be angular velocity will become zero.none of these have yielded answers.at least i want to know the end condition.so please help.
upon another rod of equal mass and in the same vertical
plane, moving with the velocity √2gc on a smooth table. If
the initial inclination of the first rod to the horizon be α, and
its length 2a, shew that it will just rise to a vertical position
if
2a (1 -sin α) (5 + 3 cos ^2 α) = 3c sin ^2 a.
i have used the fact that moment of momentum just after putting rough rod will be zero about point of contact to determine initial angular velocity.after that I used equation of energy and conservation of momentum in horizontal direction for the system.but i am not sure about the end condition, i used that reaction will become zero in vertical position and also may be angular velocity will become zero.none of these have yielded answers.at least i want to know the end condition.so please help.