|MadSci Network: Engineering|
You are both correct. The less the car weighs, the less energy it takes to accelerate to highway speeds and maintain highway speeds. Therefore you get higher gas mileage during aceleration. You can easily calculate the difference in force required to accelerate using Newton's second law of motion; F=ma. Lets say your car weighs 2000kg empty and you accelerate from a stop to 100km/hr in 5 seconds with just enough fuel to accelerate to that velocity.
To go from a standstill to 100km/hr requires an acceleration rate of 5.56 meters per second per second (100km/hr=100,000m/hr, 1hr=3600sec, 100,000m/3600sec=27.7m/sec, if it takes 5 sec to attain a velocity of 27.7 m/sec, the acceleration rate=27.7m/sec/5sec =5.56m/sec/sec). In other words, for every second that you accelerate, you will be going 5.56 m/sec faster than the second before and after 5 seconds you will be travelling at 27.7 meters/second or 100km/hr.
The force required to attain the 100 km/hr velocity with a 2000kg car would be:
F= 2000kg*5.56m/s/s F= 11,111 newtonsIf you add 60kg of fuel, the equation becomes:
F=2060kg*5.56m/s/s F=11,453 newtonsSo less fuel = less force = higher fuel economy.
Once you reach highway speeds, the difference between the full tank and the empty tank will be much less due largely to Newton's first law of motion; which states, an object in motion tends to stay in motion in a straight line unless acted upon by an outside force and an object at rest will stay at rest unless acted upon by an outside force. Once you get to highway speeds, you only have to overcome the forces of drag and friction. The shape of the car is the same whether the fuel tank is full or empty, so the drag will be the same. Friction on the other hand will vary with weight, so a heavier car will have higher friction between the tires and the road, etc.
Your wife is correct on long trips though, as the force required to accelerate is much higher than the force required to maintain velocity, and the differences in frictional forces are minimal. If you don't start out with a full tank, the multiple fuel stops and subsequent accelerations back to highway speed will destroy your economy.
So, depending on the situation, you both can be correct. For around town driving with frequent starts and stops, a less full fuel tank would give better economy. For long highway trips a full tank and fewer starts and stops will result in better economy.
I hope this is helpful.
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