The Penny Farthing Bike
"My father was also a tireless man - an inventor," said Punnish, scarcely able to contain his amusement as Pembish tried to look disapproving. "His penny-farthing bike, if you pardon the term, had metal wheels of circumference 60 and 135 centimeters respectively."
How far would you have to push this machine forward before both the wheels were again in the same position relative to the road ?
How far would you have to push this machine forward before both the wheels were again in the same position relative to the road ?
Labels: logic, mathemagic
posted by Rajesh Lal at
11:35 AM
5 Comments:
I believe it would take 4 rotations of the larger wheel.
Which is 540cm (4 multipled by 135 = 540), or 5.4 meters.
In that space the smaller wheel would have rotated 9 times (540 divided by 60 = 9).
I made the above post with 540cm as the answer...I am going to revise that.
The first time the wheels are "again" in the same position (as your question asked) is at 108cm, or 1.08 meters of travel. In that distance the small wheel would have made 1.8 rotations, and the large wheel would have made .80 of a rotation. Since both wheels are now positioned exactly 8/10th into a complete rotation; the "wheels again" are in the same position realitive to the road.
At 540cm the wheels are at the same "position again" realitve to the road. That is to say, the original starting position is "again" the same for each wheel. (e.g. each wheels starting "top dead center" is again at "top dead center".)
But you did not ask when the wheels' "positions" would be the same realitive to the road. You asked when the "wheels" themselves would be the same realitive to the road.
So, (unless you accidentally made a dangling participle in your question) the answer is 108cm of travel.
The Anon above is right. I had calculated 540 cm, but 108 would be the dist to make them relatively to each other, the same position. The 60cm wheel would have turned 648 degrees and the 135 cm wheel would have turned 288 degrees... but 648 is one revolution plust 288 degrees, so 108 cm is right.
No such thing as a centimeter during the day's of the penny farthing. Only imperial was used.
0 cm.
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