kobel51 wrote:What is the number of 360-degree rotations that a bicycle wheel made while rolling 100 meters in a straight line without slipping?
1) The diameter of the bicycle wheel, including the tire, was 0.5 meter.
2) The wheel made twenty 360-degree rotations per minute.
Dear
kobel51,
I'm happy to help.
When a wheel rolls without slipping, then during one 360-degree rotation, every point on the circumference makes contact with the ground --- this means, the wheel rolls forward a net distance of one circumference for each 360-degree turn.
We know the total distance, 100 m, so if we knew the circumference, or could find it, we could divide (100 m)/(circumference) to get the number of 360-degree rotations.
Statement #1:
The diameter of the bicycle wheel, including the tire, was 0.5 meter.
From this, we can find the circumference, and answer the prompt question. This statement, alone and by itself, is
sufficient.
Statement #2:
The wheel made twenty 360-degree rotations per minute.
Well, this introduces the element of time, which is irrelevant to the question. Perhaps it's a bicycle wheel, turning 20 rpm, and it covers the 100 meters very quickly. Or maybe its a wheel with the diameter of a pencil, turning 20 rpm, but taking a long long time to cover the 100 meters, with many many more turns of the bicycle wheel. This statement, alone and by itself, is
insufficient.
#1 sufficient, #2 insufficient. Answer = [spoiler]
(A)[/spoiler]
Does all this make sense?
Mike
