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this is common review for graduate written exam
Posted by nt moore (more from nt moore) on Wed, 8 Jan 2003 01:18:32
In Reply to: Phun with Physics (for geeks only), 2Slow, Tue, 7 Jan 2003 17:33:06
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At least that's when I first addressed it (2 summers ago) - I solved it with use of: Newton's 2nd (sum forces along radius at release angle) and conservation of energy (all potential, later potential and kinetic)
I will disagree with earlier answer - if the bead on top slides it will release at angle of 41 deg above horizontal - if the bead is solid [moment of inertia (2/5)mr^2 ] and rotates (which implies static friction) it will release at angle of 36 deg above horizontal (for the curious these angles came from arcsin(2/3) and arcsin(10/17) respectivly.
The bead flies off before the horizontal because as it rolls down the side the push of gravity on the bead, into the larger ball decreases (zero when its horizontal) and the push of gravity tangent to the ball's surface increases (mg at horizontal) Gravity's push into the larger ball [similar to what your car door does in a hard turn] is what makes the ball "turn" over the curved surface. When the push of gravity orthagonal to the surface [mg sin(theta)] is equal to the necessary push [ mass*centripital acceleration, m v^2 / Radius_of_large_ball ] the small bead will leave the surface. It leaves because gravity is't strong enough to make the bead's trajectory sufficiently curved.
Can you tell I taught this last semester?
NT
posted by 128.101.248...
Posts in this Thread:
- Phun with Physics (for geeks only), 2Slow, Tue, 7 Jan 2003 17:33:06
- I stick with repairing Saab's, this is way over my head, Anders, Thu, 9 Jan 2003 01:30:41
- I can solve this with a 12-pack and a hammer...., Richard P., Wed, 8 Jan 2003 16:54:46
- NT is right, 2Slow, Wed, 8 Jan 2003 13:22:07
- Must be in a vacuum!. Aerodynamics play a part, Texron, Wed, 8 Jan 2003 10:36:28
- this is common review for graduate written exam, nt moore, Wed, 8 Jan 2003 01:18:32 <-- Viewing This Message
- Answer, PatO, Tue, 7 Jan 2003 20:43:46
- assuming nominal friction, 90deg - motivating effect, Saabstance, Tue, 7 Jan 2003 20:33:46
- Shouldn't it always..., Dan W, Tue, 7 Jan 2003 20:12:41
- Re: Phun with Physics (for geeks only), Ken F, Tue, 7 Jan 2003 19:55:45
- Re: depends, STICKMAN, Tue, 7 Jan 2003 18:02:30
- Ahem.., K-9, Tue, 7 Jan 2003 17:35:16
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