Brain Teaser Challenge -August 2003

Butch Shadwell

Man has pondered the moon, planets and stars for all of our existence. Since the first day we started walking upright, there have been no shortage of strange theories about what these lights in the sky were and what influences they may be having on our lives. People have been killed for suggesting an unpopular explanation.

As you may know, Mars is closer to the earth than it has been for centuries and closer than is will be for centuries to come. It is a mere 30 million miles away. If beings from Mars were to want to visit, now would be the time to start heading home. So if your space ship was powered by a nuclear reactor, that had the ability to accelerate your craft at a constant rate of 9.8 meters per second squared, how long will it take to arrive and stop at Mars orbit? Fortunately, you can swing your ship around so that the thruster can be used to slow as well as speed up your ship. For extra credit, tell the highest speed you ship will reach on this trip. Let’s ignore the fact that the target is actually moving during this flight and any gravitational effects.

If you’re really feeling intelligent today, tell me the total amount of energy used for the trip in kilowatt-hours if our craft has a mass of 5000Kg. Let’s wish our Martian friends a safe journey.

Reply to Butch Shadwell by September 20 at (email), 904-223-4510 (fax), 904-223-4465 (v), 3308 Queen Palm Dr., Jacksonville, FL 32250-2328. ( The names of correct respondents may be mentioned in the solution column.

Brain Teaser Challenge Solution - July 2003

Butch Shadwell

At the time I’m writing this I haven’t received any correct responses to the last BTC. I know that publishing is delayed in some cases, so I expect to hear from more of you as the column gets out there. As you recall, after a few personal confessions, I posed the problem of charging the gate of a MOSFET to Vgson. “If you were driving the gate of a large N-channel MOSFET transistor, with a microcontroller output that has an internal resistance of 200 ohms, how long will it take to get the gate voltage up to the full Vgson of 4 volts? The CPU is running on a 5 volt supply, the FET source is at the CPU ground potential, and the gate-source capacitance of the FET is 15 pF.”

The general equation for charging a capacitor is


where Vc is the capacitor voltage after t and Vs is the supply voltage applied. If we solve for t (this is the fun part), we get


Substituting for the variables we get t = 4.83E-9 seconds. This is pretty fast, but in fact sometimes there are factors around the drain circuit that slow this down a bit, but I bet you already knew that.

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