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| Thread ID: 88253 | 2008-03-21 01:01:00 | Physics Question... | John W (523) | PC World Chat |
| Post ID | Timestamp | Content | User | ||
| 651226 | 2008-03-21 01:01:00 | A year or two back I visited the Otago Museum's Bert Munro exhibition or similiar themed event. One of the items that caught my eye was an explanation of which ball would roll the furtherest from the two optioins given. 1 - A ball droped down a straight incline with a flat smooth roll out area. 2 - A ball dropped down a curved ramp with the identical a flat roll out area. Both balls are the same size, weight and the vertical drop was the same. Roll out area was infinite in length. The horizontal distance between the start location and the bottom of the incline was the same as the curve terminated to a smooth flat roll out area. They gave the answer, but Ive forgotten as well as its explanation. Your thoughts please. |
John W (523) | ||
| 651227 | 2008-03-21 01:09:00 | Essentially the answer is... the plane won't fly. | Greg (193) | ||
| 651228 | 2008-03-21 03:32:00 | momentum = mass x velocity. Which one had the higher velocity? |
andrew93 (249) | ||
| 651229 | 2008-03-21 04:31:00 | momentum = mass x velocity. Which one had the higher velocity? but as soon a a ball starts rolling then we also have rotational inertia..... |
robsonde (120) | ||
| 651230 | 2008-03-22 02:26:00 | I would assume the ball rolling down a straight incline would pick up more speed as the sustained angle of the slope compared to a (concave?) curved slope (meets the level area's angle sooner) would naturally impart greater speed; but then again, the initial slope on the curved ramp would be steeper than the straight incline, hmm: dunno, tell us the answer :o (Maths was never my best subject :drool ) |
feersumendjinn (64) | ||
| 651231 | 2008-03-22 06:15:00 | 42 :confused: Actually given that drag will make its ugly head felt, I think the ramp which is shorter will propel the ball faster into the roll out area and therefore farther. |
dolby digital (5073) | ||
| 651232 | 2008-03-22 07:39:00 | Been over 25 years since I studied physics - but I recall mgh = 1/2mv(squared) (mass, gravity, height, and velocity). Hence accumulated energy as the ball moves comes into effect with gravity, but no sure if a curve (angular effect) would reduce the gravitational effect and hence the speed and distance... |
kahawai chaser (3545) | ||
| 651233 | 2008-03-22 10:32:00 | Naturally the iBall is classier and more expensive, even if it is a lot slower. | R2x1 (4628) | ||
| 651234 | 2008-03-22 13:44:00 | Assuming perfect rolling (no energy loss or slippage) a ball rolling down from a fixed height will end up with the same amount of kinetic energy (distributed between lateral and rotational) whatever route it gets there by. The pattern of movement makes no difference as long as no energy is lost on the ramp itself. If the ball continued to roll perfectly after the ramp, we would get in to a debate about the nature of infinities, which is more mathematical than physical. If it stops after some distance determined by momentum the two will roll the same distance from the base since the momenta are equal. If we count the whole distance traveled rather than distance from the base then the curved ramp was a bit longer so it would roll further on that scale. In other words, the question is not clear enough - the answer is 'it depends'. |
TGoddard (7263) | ||
| 651235 | 2008-03-22 21:54:00 | These deceptively simple questions....of course the plane will fly.... At school, I used to hate these sort of questions in applied maths where they used to talk about ideal this, or perfect that, and the problem either bore little resemblance to real life, and real effects were glossed over or not even mentioned. It was not until later when when deeply immersed in the analytical design of real life hydro-mechanical systems, servo systems, jet engines, etc that so-called school level "applied maths" started to make sense, but perhaps we were not taught too well. Anyway, as TGoddard says, it all depends...... 1.Friction... consider that if there was no friction, would the ball roll at all, or would it just slide??? Also if there was no friction would the ball ever stop at all??? 2.Consider, a sphere touches a plane at a point, the point has no area, therefore if the ball has weight, the contact stress may be infinite, or is it ? So now the physics of contact stresses, or 'Hertzian Stress' have to be considered. The surfaces deform and work will be done deforming the surfaces, bringing into consideration the properties of the materials such as the elastic modulii and internal damping. 3.More on friction... If the ball and incline are in a fluid medium, either a gas or a liquid, then there will be resistance to motion. If the ball does rotate, or even if it just slides, fluid will be entrapped to a greater or lesser extent between the ball and the plane. The fluid will act as a lubricant, hence the physics of lubrication of bodies in contact come into play.... "hydrodynamic lubrication" and "elastohydrodynamic lubrication". I expect there are a lot of other considerations too :rolleyes: |
Terry Porritt (14) | ||
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