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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.

Mystery of the Part-time Stud Finder: Newsletter Challenge (August 2017)

Posted July 31, 2017 5:01 PM
Pathfinder Tags: challenge question Screen

This month's Challenge Question: Specs & Techs from GlobalSpec:

Steve recently moved into a new apartment and wants to use his father’s stud finder to help put up a TV mount. It’s a nice summer day, so Steve doesn’t mind driving to his parents’ house. After retrieving it he went back to his apartment and turned it on but the screen remained blank. He changed the batteries and still it didn’t work. Steve ended up guessing where the studs were. When he finished working he tried the stud finder again and this time it turned on. Why didn’t it work the first time?

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

26 comments; last comment on 08/15/2017
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Tricky Tubes: Newsletter Challenge (July 2017)

Posted June 30, 2017 5:01 PM
Pathfinder Tags: challenge question CRT tv

This month's Challenge Question: Specs & Techs from GlobalSpec:

You are watching TV on an old television set with a cathode ray tube. It’s well-known that TV CRT’s produce x-rays as well as images. To measure the radiation dose coming from the TV set, where should you point the x-ray detector?

And the answer is:

When electrons strike the CRT they stop and produce x-rays, but they are always surrounded by an electric field (see first image below) even when they move. If an electron is brought to a sudden stop, its electric field will not completely stop or disappear. The part of the field near the electron will stop first, but the part of the field “behind” the electron does not yet know about the stop, so it continues moving toward the CRT. At the point of contact with the CRT, a “kink” or “twist” is produced in the electric field (see second image), forcing the x-rays to move sideways at an angle of 90 degrees with respect to the direction of the electron beam. There, if you want to measure the maximum available radiation, align your detector with the surface of the TV set.

36 comments; last comment on 07/21/2017
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Satellite Struggle: Newsletter Challenge (June 2017)

Posted May 31, 2017 5:01 PM
Pathfinder Tags: challenge question satellite

This month's Challenge Question: Specs & Techs from GlobalSpec:

Column 54 through 61 of a TLE set for the IRIDIUM 20 satellite has a value of -21027-4. What is this number’s meaning, and what are the physical implications of its negative value?

And the answer is:

Simplified perturbation models (SGP4 in particular) are used to determine a satellite’s orbital path. They use a standard data source known as two-line element sets (TLE). TLE sets are made available to the public by the North American Aerospace Defense Command (NORAD) for non-classified objects orbiting Earth. These data sets consist of two 69-character lines that contain all of the parameters necessary to calculate a satellite’s orbital position and velocity for a period of time around the TLE “epoch” (the moment in time corresponding to the TLE data points).

The number in the challenge question (-21027-4) represents the term of the TLE known as B* (Bstar), the ballistic drag coefficient that indicates aerodynamic drag on a satellite in the SGP4 orbit model. In aerodynamics, the ballistic drag coefficient B = CD (A/m) where CD is an object’s coefficient of drag, A is its cross-sectional area, and m is its mass. When B is modified by a reference value for atmospheric density, ρo, B* is obtained: B* = Bo /2). B* represents an object’s susceptibility to drag.

Negative B* values occasionally show up in TLE sets, indicating erroneously that energy is somehow being added to the system. This is not the physical reality of drag acting on a satellite, of course. It is instead a consequence of the way SGP4 models forces with respect to the actual dynamic environment. From Revisiting Spacetrack Report #3 [PDF], we know that “SGP4 uses power density functions that require a term that encapsulates the ballistic coefficient, B*. Simplified force modeling and the batch-least-squares processing of observational data often yield a B* that has “soaked up” force model errors.”

The full TLE set for this challenge question was:

IRIDIUM 20 [+]

1 25577U 98074A 17107.88627323 -.00000039 00000-0 -21027-4 0 9999

2 25577 86.3914 280.5847 0002046 90.5751 269.5679 14.34214463145187

For more detail on the two-line element set format used for satellite tracking, see T.S. Kelso’s FAQ on the topic.

3 comments; last comment on 05/31/2017
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Frustrating Fastballs: Newsletter Challenge (May 2017)

Posted April 30, 2017 5:01 PM
Pathfinder Tags: baseball challenge question

This month's Challenge Question: Specs & Techs from GlobalSpec:

Once in a while you may hear a baseball player describe a pitcher’s pitch as a “rising fastball.” This seems to violate the laws of physics because a baseball is subject to gravity and should immediately have a downward acceleration, in addition to its forward acceleration, when released by a pitcher. Thus a pitch that rises should be impossible. What’s going on?

And the answer is:

Batters divide a pitch into thirds. During the first third the batter is picking up the ball after the pitcher releases it. The second third has the batter anticipating the timing and location of the swing needed to hit the ball. Finally the third part is the batter swinging the bat. So when a pitcher throws several 90-mph fastballs in a row, the batter develops a mental model for the trajectory of that pitch. Baseball announcers will often call this “getting the pitcher’s timing down.”

Some pitchers will occasionally throw a faster version of their fastball to throw off the batter’s timing. For example, that pitcher throwing 90-mph might slip in a 95-mph fastball one pitch. The batter picks up the ball but doesn’t notice the 5 mph difference in speed. The batter calculates where the 90-mph fastball would go and swings at that spot. But the 95-mph fastball has a flatter trajectory. It doesn't drop quite as much from the pitcher to plate because it's going faster.

This results in the batter swinging under the pitch. The pitch appears to be higher than the batter expects and to the batter the pitch seems to “rise”. Thus the rising action sometimes described by hitters is actually a result of mental miscalculation. Crafty veteran pitchers will sometimes exploit this effect by subtly varying their pitch speeds by using modified grips.

27 comments; last comment on 06/02/2017
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Baffling Beer Glasses: Newsletter Challenge (April 2017)

Posted March 31, 2017 5:01 PM
Pathfinder Tags: beer challenge question optics

This month's Challenge Question: Specs & Techs from GlobalSpec:

Typical beer mugs have thick walls and a thick bottom. This design serves two purposes. First, it makes the mug heavier, so the drinker assumes the beer is “good.” The second reason is to give the impression that the mug holds more beer than it actually does. Why is this so? Why would the volume appear greater than it is?

And the answer is:

This is an illusion caused by refracted light coming from the beer and passing through the glass and then moving into the air. See, for example, the following figure in which a ray leaves the left edge of the beer. When the ray reaches the edge of the mug it bends when it reaches the air near a viewer’s eyes.

When the viewer’s eyes interact with the ray they mentally extend it back into the glass (mug) and conclude that the original start of the ray is to the left of the actual starting point, as shown in the figure. The mug appears to have a bigger diameter, so the drinker assumes they will enjoy more beer than they actually paid for. Of course, the bartender is happy!

27 comments; last comment on 04/25/2017
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