ShmoopTube

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All right here's your shmoop du jour brought to you by little tiny people.

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Sure it would be irresponsible to rule over an island full of 6-inch tall people but [Giant man kneeling over tiny people]

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probably also feel pretty cool at least for a while. All right check out the [Giant man tied to the floor by all the small people]

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following picture, this drippy thing here. All right in the satire Gulliver's [Picture of a mug on its side dripping water onto a cog]

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Travels the main character ends up on the island of Lilliput which is

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inhabited by tiny people. To supply power to the island the Lilliputians chief

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electrical engineer has rigged that tiny paddle wheel with a radius of 3

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centimeters to a motor that generates power. Waterfalls spin the wheel and a

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single water droplet hits each paddle. Each water droplet is 1 gram which is

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enough to move the paddle. Which of the following changes to the system will

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result in a larger power output and here are the potential answers. [Potential answers appear]

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Let's get these folks some more power so they can charge their tiny iPhones and [Static ball]

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blast their teeny little air conditioners. Well Lilliput gets pretty

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warm this time of year you know... Well torque equals force times the distance

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from the axis at which the force is applied on the spinny thing, multiplied [Water wheel spinning]

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by the sine of the angle created by the force vector and whatever part of the

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spinny thing the force is being applied to. Well spinny thing by the way is a

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special physics term... So which of the answers will increase the right side of [Man studying at a computer]

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this equation. Well (A) definitely will not do it. If we decrease r we'll only

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decrease the torque, same thing with answer B if we decrease the mass of the

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water droplets we'll be decreasing the force acting on the wheel. After all the [Red cross drawn over answer B]

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force of the falling water is coming from the force of gravity decrease mass [Man in a pool under a small waterfall]

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and you'll be decreasing the force of gravity right alongside. And answer (D) is

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really a zero-sum situation if two drops hit half the paddles well the total [Red cross drawn over answer D]

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force is going to remain about the same. But if we move the paddle so the water

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is hitting farther from the center then we're increasing that radius. Remember R [Man pulls the wheel to increase the distance]

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doesn't mean the total length of the moment arm it means the distance from

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the center of the wheel and where the force is being applied.

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Its like if you have a five meter long lever and you only push on it at the 1 meter [Lever appears]

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mark you basically just made yourself a 1 meter lever. Well those other 4 meters [Hand pushes on the lever]

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of lever aren't doing you any good moving the force farther from the center

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means a bigger R and that means more torque so the correct answer is (C). Okay [Hand pushes on the end of the lever]

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there little dudes plug in your tiny little electric cars and crank up those

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cute little washing machines, if only we could solve our energy problems with the [Tiny car drives next to man tied down]

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you know a few drops of water...

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