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Challenge Questions

Stop in and exercise your brain. Talk about this month's Challenge from Specs & Techs or similar puzzles.

So do you have a Challenge Question that could stump the community? Then submit the question with the "correct" answer and we'll post it. If it's really good, we may even roll it up to Specs & Techs. You'll be famous!

Answers to Challenge Questions appear by the last Tuesday of the month.

Baseball Spin: Newsletter Challenge (February 2016)

Posted February 01, 2016 12:00 AM
Pathfinder Tags: baseball challenge questions

This month's Challenge Question: Specs & Techs from IHS Engineering360:

Suppose you are a professional baseball batter (maybe Alex Rodriguez?). You are looking at the pitcher (Sandy Koufax?), and you claim that you can see the spin on the ball throughout its trajectory from its release from the pitcher's hand to when you strike the ball with the bat. Is this true or it is simply a "ball-park" lie?

The answer to this challenge will be posted later this month, right here on CR4.

27 comments; last comment on 02/09/2016
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Handel's Tune: Newsletter Challenge (January 2016)

Posted January 01, 2016 12:00 AM
Pathfinder Tags: challenge questions

This month's Challenge Question: Specs & Techs from IHS Engineering360:

A time traveler went back to 1742 and kidnapped George Frideric Handel so he could bring him to the Kennedy Center in NYC in December of 2015 to enjoy his masterpiece Messiah, played by the National Symphony Orchestra. As soon as the first notes are played Handel cringes and shakes his head. What's wrong?

And the answer is:

Handel doesn't like the pitch, which to his trained ear sounds sharp. Modern orchestras use a tuning standard of 440 Hz for A above middle C. However, this has not always been the case. This standard has varied by as much as 50 Hz over the years. A tuning fork from 1740 associated with Handel has been found to have a frequency of 422.5 Hz. Handel's Messiah was composed in 1741 and likely followed this tuning convention. Thus the modern orchestra would sound sharp to Handel. Still, once Handel adjusted to the higher pitch, he no doubt would have appreciated the National Symphony Orchestra's playing of his work. Music has much less to do with pitch than it has to do with the intervals (differences between pitches).

43 comments; last comment on 01/26/2016
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Three Spheres: Newsletter Challenge (December 2015)

Posted November 30, 2015 12:00 AM
Pathfinder Tags: challenge questions

This month's Challenge Question: Specs & Techs from IHS Engineering360:

Consider three identical metal spheres, with diameters of 20 cm. Arrange them in a straight line, as shown. Each two consecutive spheres are connected by an extremely small diameter conducting wire.

If the potential at the center of each sphere is the same, determine the charge in each sphere. The sum of the three charges is Q.

And the answer is:

The potential at a charged sphere is given by

where R is the radius of the sphere.

Because of the symmetric arrangement spheres A and C must have the same charge, if both have the same potential. Let q be this charge; so qA = qC = q

Let the charge at sphere B be qB. Then the potential at its center is given by

The potential at each spheres A and C is given by

We also know that

And

So equating the first two equations yields

Then,

Or,

but from the total charge equation, we have

Substitute this into the previous equation and solve for q to get

Therefore

Or

16 comments; last comment on 01/27/2016
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Tropical Cyclone No Fly Zone: Newsletter Challenge (November 2015)

Posted November 01, 2015 12:00 AM

This month's Challenge Question: Specs & Techs from IHS Engineering360:

Northern Australia gets hit by several tropical cyclones every year, as does the Philippines. Directly between Northern Australia and the Philippines lies Indonesia which almost never experiences any tropical cyclones. Why?

And the answer is:

The Earth rotates faster at the equator than near the poles because the Earth is wider at the equator. This causes the Coriolis effect, an apparent deflection of moving objects when measured within the Earth's spinning reference frame. This is the reason why tropical cyclones in the Northern Hemisphere spin counter-clockwise and in the Southern Hemisphere spin clockwise. Any tropical cyclone that straddles the equator (and thus is in both the North and South Hemispheres at the same time) tries to spin both clockwise and counterclockwise, and rips itself apart. In addition, the clockwise moving storms are deflected south while the counter-clockwise storms are deflected north. The result is a "no fly zone" for tropical cyclones close to the equator, which is where Indonesia lies.

See image below:

12 comments; last comment on 11/03/2015
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Pack Your Bags: Newsletter Challenge (October 2015)

Posted October 01, 2015 12:00 AM
Pathfinder Tags: challenge questions

This month's Challenge Question: Specs & Techs from IHS Engineering360:

You are a regular hiker. When you pack your backpack you decide to put the heavier items close to the bottom of the backpack and the lighter, less dense items near the top. Is this the best way to pack? Is this scheme good for your body?

And the answer is:

No, this is not the best way to pack your backpack. You should put the denser, heavier items at the top of the backpack in order to keep a high center of gravity. Maintaining a high center of gravity in the backpack prevents large bending angle at your waist. A smaller bending angle means less strain on the back muscles and the stomach. Some native tribes have perfected carrying heavy loads on their heads so that no forward bend is needed.

59 comments; last comment on 10/31/2015
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Mars Farms: Newsletter Challenge (September 2015)

Posted September 01, 2015 12:00 AM
Pathfinder Tags: challenge question

This month's Challenge Question: Specs & Techs from IHS Engineering360:

A group of settlers are debating possible locations for a Mars colony. All proposed settlement sites are located in the northern hemisphere. When asked why this is, the settlers responded "For the longer growing season." Why would one hemisphere of Mars have a longer growing season than the other?

And the answer is:

Mars has approximately the same tilt as the Earth (Mars = 25° vs Earth=23.5°). So just like Earth, Mars has seasons depending upon its position in its orbit. However, compared to Earth, Mars has a very elliptical orbit (Mars = 0.094, Earth=0.017). That means the length of the seasons vary more than on Earth due to changes in orbital speed as Mars orbits the Sun. In the northern hemisphere of Mars, the seasons are as follows:

Spring - 7 months
Summer - 6 months
Fall - 5.3 months
Winter - 4 months

The situation is reversed in the southern hemisphere of Mars where Spring lasts 5.3 months, Summer lasts 4 months, Fall lasts 7 months and Winter lasts 6 months.

Thus the growing season is longer in the northern hemisphere of Mars.

74 comments; last comment on 12/20/2015
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