Quote:
Originally Posted by knucklesplitter
Note that it does not say the "surface speed of the wheels' outer diameter", it says the "speed of the wheels".
If the plane is at rest, the wheels are too - going 0mph, and the conveyor belt is not moving either.
If the plane is going 5mph, the wheels are also going 5mph (right along with the plane they are attached to no matter how fast they are spinning). The conveyor belt is going -5mph (the "-" meaning the opposite direction). If the plane had a speedo connected to the wheels it would falsely read 10mph. You would use 10mph to calculate the RPM of the wheels given the diameter.
If the take-off speed of the plane is 150mph, the wheels are also going 150mph (moving right along with the plane). The conveyor belt is going -150mph. If the plane had a speedo connected to the wheels it would falsely read 300mph. You would use 300mph to calculate the RPM of the wheels given the diameter.
Whenever you talk about the speed of one thing versus another, like say a wheel versus a conveyor belt (note it says "belt" not roller nor the whole conveyor), you have to use the same units of measure. I have designed and spec'd 100's of conveyors. When you talk about conveyor belt speed the unit of measure is m/sec, or feet/sec - in other words linear speed which of course mph is. Rotational speed is not the same thing - an object can be spinning at 1000 rpm and still be going 0m/sec (like a house fan for example). So if you are going to say that a conveyor belt is going "to exactly match the speed" as a wheel it has to be in linear speed units.
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Well, whenever I've run my fat ass on a conveyor belt, it clearly displays the MPH that I'm running, so obviously when you know the size and distance of the rollers (from eachother), you can determine the speed (in MPH) of the belt. Additionally, when the wheels of a vehicle spin, it's possible for a speedometer to use their RPM as a way to display MPH. The speedometer isn't displaying the speed at which the wheels are traveling through the air, it's displaying the speed (albeit theoretical speed) of the outside diameter of the tire.
When I read the question, I believed it was referring to the above type of measurements when it uses the word "speed". I certainly defer to those of you that obviously know more about physics based terminology than I do.
However, I do maintain that if if the word "speed" in the problem refers to rotational speed at the outside of the wheels (RE: what typical speedometers in cars and trucks display), without a harrier or a slipping tire, the plane is prevented from moving forward by the constraints of the problem (RE: wheel speed is matched by conveyor in opposite direction).
Furthermore, as soon as any thrust is exerted on the plane at all (presumably by the props/jets), the wheels would instantly accelerate to infinite MPH and SECCS would implode into a blackhole that sucks my brain out through my nose.