In each issue of the Automation Notebook we feature a section of brainteasers. These are the brainteaser answers from Issue 22, 2012 of the Automation Notebook. The brainteaser questions are repeated in black. The answers to the brainteaser questions are highlighted in red with explanations. You can view the brainteasers from Issue 22, 2012 without the answers here:http://library.automationdirect.com/brainteasers-issue-22-2012/
1. Alignment Time
On a functioning clock, the hour and minute hand are perfectly aligned (superimposed, not opposed) several times each day. Can you determine a formula to calculate those times? How about for the minute hand and a sweep-second hand? How about for all three hands?
Answer: In a 12 hour period, the minute and hour hands align 11 times at equally spaced intervals. So the interval is every 12/11 hours, or 1:05:27.273. The formula 12/11x (where x is an integer from 1 to 11) will generate the following unique times for each 12 hour period (you may find it more convenient to use 43,200/11x and read the answer in seconds):
1:05:27
2:10:55
3:16:22
4:21:49
5:27:16
6:32:44
7:38:11
8:43:38
9:49:05
10:54:33
12:00:00
The minute hand and a sweep second hand will align 59 times every 60 minutes (every 61.017 sec). So the formula 60/59x (where x is a non-zero integer) yields answers in minutes (use 3600/59x for answers in seconds).
Assuming that all three hands are perfectly aligned at noon, the only other time they will align each day is at midnight. If you look at the list of times given in part one of this question, you can see that whenever the hour and minute hands are aligned, the second hand is always at least 5 seconds away.
2. Real-Time Conversation
A man in Florida decided to call his friend in Oregon. During the conversation he mentioned what time it was. The woman in Oregon said, “You mean here in Oregon?” The man in Florida said, “No, that’s what time it is here in Florida”. The woman, still in Oregon, said, “That’s odd, that’s exactly what time it is here, also!” Both were right. How can this be?
Answer: It is the first Sunday in November between 1:00 am and 1:59 am. The man in Florida lives in the small western portion of the “panhandle” that is on Central Time, not Eastern Time. The woman in Oregon lives in the small eastern portion of Oregon that is on Mountain Time, not Pacific Time. Both of these states observe Daylight Savings Time (DST). Central Time and Mountain Time would be the same during the hour when the clocks have been set back an hour in Central Time, but before they have been set back in Mountain Time (during the transition from DST to standard time in the fall).
3. Chime Time
If a clock takes 7 seconds to strike 7:00, how long will the same clock take to strike 10:00?
Answer: If it takes 7 seconds from the beginning of the first strike until the end of the seventh strike, then each of the six intervals lasts 7/6 seconds. When striking 10:00 there are 9 intervals, so the answer is 9*7/6 = 10.5 seconds.
4. Automagic Controls?
Fred spent a few minutes last week and added an AutomationDirect component to his factory’s control system. He made no electrical connections whatsoever to this device, but still the machine’s operators were delighted with the real-time information this device provided. Do you know what this helpful device was?
Answer: This current sensing device has no electrical connections. A current carrying wire must pass through the center hole in this device but they need not even touch. When current flows in the wire, the LED flashes. The LED is powered completely by the electromagnetic field of the wire in question.
ACL1: (AC CURRENT INDICATOR, 0.5-100A RANGE, RED FLASHING LED)
AcuAMP AC current indicator, 0.5-100A indicating range, flashing red LED when AC current is present, UL 508 listed
Automation Direct offers the full line of AcuAmp™ switches and analog current sensors based on this same principle (some do require a separate power source).
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