- #1
A13235378
- 50
- 10
- Homework Statement
- Consider a dumbbell formed by two equal balls and a rod of negligible mass and length l, positioned vertically on a flat and horizontal table. A horizontal and instantaneous speed is communicated to the bottom ball. Determine the highest value of this speed so that the bottom ball does not lose contact with the table.
- Relevant Equations
- Energy conservation
T = I . a , T = resulting torque , I = inertia momentum, a =angular acceleration
Attempted solution:
Consider the instant when the normal force of the lower ball is zero. Conserving energy:
$$\frac{mv^2}{2}+mgh_1=\frac{mv_1^2}{2}+\frac{mv_2^2}{2} + mgh_2$$
Applying the resulting torque to the upper ball where the rotation point is the lower ball.
$$T=I.a = ml^2.\frac{v^2}{l}$$
From that, I crashed because there are many parameters. Furthermore, I cannot draw any conclusions and information at the moment when the normal force becomes zero
Can anybody help me?
I just need you to have a little patience and understanding, because I'm still a very beginner in this dynamic part of the rotation
Consider the instant when the normal force of the lower ball is zero. Conserving energy:
$$\frac{mv^2}{2}+mgh_1=\frac{mv_1^2}{2}+\frac{mv_2^2}{2} + mgh_2$$
Applying the resulting torque to the upper ball where the rotation point is the lower ball.
$$T=I.a = ml^2.\frac{v^2}{l}$$
From that, I crashed because there are many parameters. Furthermore, I cannot draw any conclusions and information at the moment when the normal force becomes zero
Can anybody help me?
I just need you to have a little patience and understanding, because I'm still a very beginner in this dynamic part of the rotation