Suppose you go to the gas station to fill up your tank which costs 30 dollars. At $2 per gallon that fill-up bought you 15 gallons. Your vehicle travels an average of 18 miles per gallon giving you a distance of 270 miles before your next fill-up. Your vehicle’s gross weight is 5,000 pounds including driver. On your way to the vehicle, out of the gas station you find a nickel on the ground…
Given the weight of a nickel is 5 grams. and the value of a nickel is obviously 5 cents, how many miles would you have to travel before the extra weight of that nickel impacts your miles per gallon in a way that would cost you an extra five cents. (Given everything else remains a constant)
You can go forever. The five grams is insignificant compared to the 5000 #. When you say 5000# you are either saying 5000 +/-1 or 5000 +/- 10 etc. All of which make the 5 grams insignificant. Does your gas consumption go down because you drink a soda or buy a big mac?
I have assumed that the additional weight of the nickel decreases the gas mileage in a linear fashion. This is almost certainly not true. But here’s a start.
At 18 mpg, a 5000 pound car is getting 90,000 pound-miles per gallon.
$0.05 at $2 per gallon buys 0.025 gallons of gas
0.025 gallons of gas should give you an additional 2250-pound miles.
According to Google, 5 grams = 0.011 pounds
2250 pound-miles should move 0.011 pounds 204,545.4.
A nickel does have a mass of 5 grams. (I checked it).
A 5000 pound car weighs 2,268,000 grams.
The car can travel 270 miles for $30 or (dividing by $30), it can go for 9 miles for every $1 of gas OR can travel .45 miles for a nickel’s worth of gas.
The car weighs 454,000 times more than a nickel.
Therefore the mass of a nickel would COST a nickel after 454,000 * .45 miles which equals 204,300 miles. Which would be the “break-even” point.
You did ask when it would cost an EXTRA nickel so I guess it would be 408,600 miles.
darn you Igloo
I got beaten to the punch (or the post)
Seems we agree on the mileage. I wonder if blaneg2 meant a break-even point OR an extra nickel? (If so, I might have the right answer??) Well, I posted both just to be sure.
Okay, but what if somebody in the car was on the Atkins diet? And, thank goodness it was stated when the nickel was picked up (and we’ll assume the engine wasn’t running while he/she was wasting their time picking up a nickel). Can you imagine the calculations required if it was picked up at some inprecise location along the way? Speaking of linear response, the car gets lighter as the gas is consumed. Just stirring the pot.
Not all of these things depend on weight. The above calculations have assumed that a given amount of gas yields a certain (mass)(distance), implying that a car made of magic weightless material would get infinity miles per gallon, which isn’t the case. Instead, a given amount of gas yields a certain
(mass)(distance) + (a term for wind resitance) + (a term for stopping/starting which will involve mass) + (etc.)
A linear approximation probably works quite well (especially for such a small perturbation), but not with an intercept at zero.
Now, if someone were to dig up some data on fuel economy versus vehicle weight, we could fit a line to it and go from there. Short of that, you’ll need to determinine all those other terms first.
