- #1
Petrulis
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Homework Statement
Here is the drawing which shows the situation:
http://img507.imageshack.us/my.php?image=drawingae3.jpg
The mass of each ball is equal to m. A rod which connects the balls is weightless. A vertical wall affects a ball which is below with force F. I need to find this force when the angle between the rod and ground is alfa (the rod is vertical at the beginning).
The Attempt at a Solution
Stress in the rod T.
Potential energy of the right ball is
PE = mgR sin(α)
Kinetic energy of the right ball is
KE = 1/2 m v²(α)
Conservation of energy:
KE + PE = Eo
1/2 m v²(α) + mgR sin(α) = mgR
v²(α) = 2 gR (1 - sin(α))
Centripetal accleration:
a(α) = v²(α)/R = 2g(1 - sin(α))
Balance of force along the rod:
ma(α) = mg sin(α) - T(α)
2mg(1 - sin(α)) = mg sin(α) - T(α)
mg(2 - 3sin(α)) = -T(α)
T(α) = mg(3sin(α) - 2)
Answer:
F(α) = T(α) cos (α) = mg(3sin(α) - 2)cos(α)
But the last equation means that if α<arcsin(2/3) = 41.8 deg, the left ball will no longer touch the wall. Is it possible? Maybe there are some mistakes in the solution?
Thanks in advance.