There is a circular railway track.The circumference of the inner track is 100m and that of the outer track is 125m.On 1 complete revolution by a train the wheels on the inner track cover 100m and obviously the wheels on the outer track travel 125m. This means that the speed of the inner set of wheels was less than the outer ones.But both of the wheels are attached to the same axle.Then how is this problem solved.
Please I need detailed and convincing answers.
2006-12-21 23:45:54 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Physics
A good question.Perhaps it can be explained this way.
Since both the wheels are attached to the same axle both the wheels will make equal number of revolutions.But the difference may be one of or a combination the following acts:
1.Since the wheels travel in a circular path there will be a centrifugal force If the speed is sufficient enough the outer wheel being unable ,to drift away, will try to lift itself.In such case the outer wheel will not touch the outer rail.
2.If the speed is not sufficient there will be a drag on the outer rail.
In fact in the case of sharp curves the outer rail will be laid slightly raised to enable higher speeds.This can be observed by you in highway curves where the outer side of the bend is raised sufficiently .
2006-12-22 03:01:55 · answer #1 · answered by karikalan 7 · 1⤊ 1⤋
This is exactly why cars are built with differentials. You are exactly right in saying that the outside wheel has to travel farther. Also angular motion has nothing to do with this problem. There are two possible scenarios for this problem. The first, although not likely is that if this train will always be on the circular track, you can make the outside wheel slightly larger. If the ratio of wheel diameters is 100:125 or 1:1.25, the train will move smoothly along the tracks. However, this is not a realistic situation. No one really does this. The other option is that if the wheels are the same size, then they must slip on the track a bit. I am assuming they are made of the same material, and therefore have the same coefficient of friction. To solve this problem you would have to assume that they slip equal amounts and therefore travel an average of 112.5 meters. Realistically speaking though, you know that the coefficient of kinetic friction is less than that of static friction. This implies that whichever wheel slips first would remain slipping the entire time until the train stopped. In reality, which wheel would slip first? Your guess is as good as mine.
Note: What the heck is up with Varunjay!!!!! He just copeid my answer!!! Thats not cool!!!
2006-12-22 09:01:29 · answer #2 · answered by Andy M 3 · 0⤊ 0⤋
Fortunately the wheels can slip on the rail. Proportionately both the wheels will slip on the track and adjust by itself.
In long run this will cause excessive wear and tear for the tracks and the wheels.
So modern coaches are having independent wheels.
If the wheels can independently rotate on the axle, no slippage will take place outer one will turn more than the inner one.
2006-12-22 14:23:15 · answer #3 · answered by dram2007 1 · 0⤊ 0⤋
You don' t have to worry about the speed in this one because it is obvious that they are not moving at the same rate. However, look at the fact that as the inner tires travel a certain distance, the outer ones are traveling a larger distance because the ANGLE of the vehicle is changing. Its like, why can you put a compass with two points (to make concentric circles) on a piece of paper, and have both tips make two perfect circles. the angles are changing so the outer one travels more distance in the same time. Therefore, the acceleration of the outer wheel is greater than the acceleration of the inner wheel because acceleration is the change in distance divided by the change in time.... good luck.
2006-12-22 07:57:26 · answer #4 · answered by Anonymous · 1⤊ 2⤋
What the h--- kind of railroad is this? To fit your description, the rails would have to be 3.979 m (>13 ft) apart! Not to mention the inside rail has a radius of only~ 15 m.......
What exactly do you mean by 'solving' this 'problem'? Railroad car and engine wheels have slipped going around curves for over 150 years. I don't know about modern coaches, but the overwhelming majority of cars on US lines are for freight and have solid axles.
In this case, the inside wheels would probably slip because the centrifugal moment would result in less normal force on the inside rail.
2006-12-22 22:03:07 · answer #5 · answered by Steve 7 · 0⤊ 0⤋
A good Q and i use to think about a similar one which is more challenging to explain. Imagine any 2 points along the radius of a wheel or a coin and they travel the same distance after n nr of rotations, if you imagine 2 parllel lines from start to finish. But it is different, if you mulitiply the circumference and the nr of rotations.
2006-12-22 10:15:49 · answer #6 · answered by Anonymous · 0⤊ 1⤋
YOU NEED TO UNDERSTAND CONCEPT OF DIFFERENTIAL(mechanics)
Although i am giving example of a vehicle same is applicable for a train.
A vehicle's wheels rotate at different speeds, especially when turning corners. The differential is designed to drive a pair of wheels with equal force, while allowing them to rotate at different speeds. In vehicles without a differential, such as karts, both driving wheels are forced to rotate at the same speed, usually on a common axle driven by a simple chain-drive mechanism.
2006-12-22 08:23:51 · answer #7 · answered by Som™ 6 · 1⤊ 0⤋
the wheels on inner trach wear out quickly....the question is obvious..producing a turning effect on the train wheels...
2006-12-22 11:44:48 · answer #8 · answered by anvesh reddy 2 · 0⤊ 0⤋