Brain Teaser Challenge - April

by Butch Shadwell

I was asked to give a talk this evening at the local community college for an advanced astronomy class. My lecture today was about radio astronomy and some of the physics and technology that is applied to that field. I spoke about the electromagnetic spectrum in general and some of the key features of light and radio wave propagation.

We were discussing the ubiquitous parabolic dish that is used in radio telescopes. If our dish is 9 feet wide and is one foot deep from the edge to the belly along the center axis, can you calculate the focal length? Placing our receiver at this point will focus all rays parallel to the center axis on the antenna feed horn. Maybe we will pick up TV from space.

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The names of correct respondents may be mentioned in the solution column.

Brain Teaser Solution - March

Last month I was trying to make sense of the trade-offs that are accepted by those folks that choose to put these huge boom sound systems in their cars. In my hypothetical case “…we start with a Scion sedan that weighs 1800 pounds (*with driver). … And we will say the little engine produces 90 horsepower. For this calculation we will assume that there is a linear relationship between the mass of the vehicle and its miles per gallon of fuel, and the rate of acceleration at a given engine available horsepower. So if this car normally can get from 0 to 60 mph in 9 seconds and gets 35 mpg, what would the stats be if we added a 350 pound sound system that pulls 10,000 watts?”

To calculate the loss of acceleration you need to first figure out the available horsepower. With 10,000 watts (13.4 HP) wasted on the sound system, there is only 76.6 HP remaining to accelerate the car. Using a simple ratio-metric calculation, if the mass of the car was unchanged the new 0 to 60 time would be 10.57 seconds. However since the mass is increased by 19.4% the time is also that much longer, or 12.63 seconds. In reality predicting the miles per gallon is much more complicated. While doing an acceleration test run the engine is pretty much running at full power all of the time. However, a cruising vehicle uses only a fraction of that power. In general the average MPG is dependent on the mass of the car and the change is inversely proportional to the increase in mass. MPG1/MPG2 = Mass2/Mass1, so MPG2 = (MPG1*Mass1)/Mass2. MPG2 = 29.3 is the new mileage with the added weight of the sound system and the stereo off. Depending on the kind of driving, turning on the stereo in the car could lower gas mileage to less than half of that experienced normally. To make up for this loss in performance, they better be some very good tunes. But I bet you already knew that.