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Rover
Yahoo User
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 Posted: Tue Feb 19, 2008 4:52 am Post subject: Help needed please with a simple physics/ engineering problem? |
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| Hello. I was looking through a puzzle book the other day and one question had me stumped. See if you can help.Imagine a diagram of a bicycle chain and gears. The pedals are attached to a big cog, with the chain leading to a very small cog.The next diagram is identical, except the rear cog is slightly larger. The last diagram is identical again, but with the rear cog larger still, so it is only a fraction smaller than the front gear. The question then reads; which of these gears would be best for cycling up a steep hill?I would have said the first one, because for each time you pedalled the rear cog (and therefore the rear wheel) would move through more rotations, therefore getting up the hill easier. However the answer is the third cog, the largest; is this right? If so, please explain? |
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Mista Ricksta
Yahoo User
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| Posted: Tue Feb 19, 2008 4:58 am Post subject: |
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| YOUR answer would be correct for going DOWN the hill!Haven't you ever RIDDEN a ten-speed bike? You can do this experiment on your OWN if you can get onto one of these and see for yourself why the largest sprocket is the best sprocket to use when traveling uphill.You are forgetting EVERYTHING you know about mechanical advantage. When going uphill, you want the GREATEST mechanical advantage and you get this by using the largest sprocket you can on that rear wheel. |
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paul m
Yahoo User
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| Posted: Tue Feb 19, 2008 4:59 am Post subject: |
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| rear cog is the drive so yes the bigger the rear cog, the easier it would be to peddle. |
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Joe U
Yahoo User
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| Posted: Tue Feb 19, 2008 5:02 am Post subject: |
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| If the drive gear is smaller than the driven gear (read sprocket wheels for gears) then the drive gear has the mechanical advantage, in the specific ratio of the two diameters. |
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dbrads
Yahoo User
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| Posted: Tue Feb 19, 2008 5:05 am Post subject: |
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| The answer has to do with torque. Torque is basically the force applied to an object to make it rotate. The amount of torque that is applied to the rear gear is equal to the torque applied to the front gear multipied by the ratio of the gear radii (rear gear / front gear). Therefore as the rear gear gets bigger, more torque is applied to the rear gear. The more torque applied to the rear gear the easier it is to move up a hill. The first scenario with the smaller gear is used for level or downhill when you dont need as much torque. You would get more revolutions on the rear gear giving you more speed. |
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scooterboy
Yahoo User
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| Posted: Tue Feb 19, 2008 5:06 am Post subject: |
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| its in regards to pulleys and ratios. the third cog is one to one (almost) so the energy to turn the back wheel is equal to the front but the first cog is closer to 3/1 IE you need three times the energy to rotate the wheel. IE the front wheel has to turn three times to the rears once and as the person said the rear is the drive wheel so ideally you need a larger cog on the rear wheel than the front pedals so it would be easier to go up hill.easy mistake |
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rs
Yahoo User
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| Posted: Tue Feb 19, 2008 5:13 am Post subject: |
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| yes you are correct the third would be the best however only for someone with who has limited power to weight ratio. the seccond or third would be better for someone with a greater power to weight ratio.it would take more rotations of the third set to achieve the distance as the first given the same ammount of rotations |
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Pit Bull
Yahoo User
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| Posted: Tue Feb 19, 2008 5:17 am Post subject: |
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| Think about gearing.......if front and rear sprockets were the same size then one turn of the pedals would equal 1 revolution of the wheel. [Low gear for going uphill]. If the back sprocket had say 16 teeth and the front had 48 then one pedal revolution would turn the wheel 3 times. [Higher gear for level or downhill...much easier pedalling].PS there's no such thing as a 15 or 18 speed bicycle because a gear ratio of 48/48 is the same as 32/32......it's simply an identical and duplicate gear. What makes the difference is cadence, the speed which the pedals turn at. Similar to a car engine going through the gears and increasing or decreasing speed while the engine revs stay much the same.Sorry if I've overcomplicated things but it may help. |
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th83
Yahoo User
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| Posted: Tue Feb 19, 2008 11:03 am Post subject: |
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| the way i see it if both were the same size then the rear wheel would go round once each time you pushed the pedals round once, ok. if the rear cog was very small it would go round lots more times each revolution of the pedals, this would mean you were going further therefore faster for each revolution. so this must be harder so the bigger cog both ends must be easier. does this make sense? |
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