On May 23, 1998, a tanker truck loaded with gasoline (p=719.7 kg/m^3) jumped a j

Question

On May 23, 1998, a tanker truck loaded with gasoline (p=719.7 kg/m^3) jumped a jersey barrier and collided with an oncoming pickup truck. The resulting fireball and blaze melted structural supports of the I-95 bridge near Philadelphia on which the crash occurred. Hypothetically, upon leaving the filling station, tire pressure for each tire on the 18-wheeler was measured as 105 psi (gauge), and the wheel contact area with the ground was a 6.0 in by 7.0 in rectangle.

If the weight of the empty truck and tanker was 120 kN, please calculate the volume of gasoline in the tanker at the time of the crash in m^3. Furthermore, at today’s gasoline price of $2.58/gal, plus the cost of the 18-wheeler (purchase price of $98,000.00), what was the total economic loss to the shipper?

Explanation / Answer

For this problem, we are going to have to do a lot of conversions to get the mass of the truck with and without gasoline. After, we will have to find the volume of the gasoline to obtain the price and add it to the price of the 18-wheeler.

Mass of empty truck:

The weight is 120 kN. This is a measure of force, specifically, the force of gravity.

F = ma = mg

120E3 N = m*(9.8 m/s2)

m = 120e3/9.8 kg = 1.22E4 kg

Mass of truck with gasoline:

Pressure = force/area

Each tire shares an 18th of the force of the vehicle. If we find the force each tire exerts against gravity (that is, its weight), we can use this to find the mass.

105 pounds/in.2 = F/(6.0 in. * 7.0 in.) = F/(42 in.2)

F = 4410 lbs.

We can convert this directly to mass in kg using a conversion factor (keep in mind that this conversion factor has within it the acceleration due to gravity, so that's how we convert from a force to a mass)

m = 4410 lbs. * 0.454 kg/lb. = 2000 kg

Now, that's the mass of an eighteenth of the truck. To get the full mass, we must multiply by 18

m = 18*2000kg = 3.60E4 kg

Volume of the gasoline:

First, we need the mass of the gasoline, which we obtain by subtracting the mass of the full truck from that of the empty one:

3.60E4 - 1.22E4 = 2.38E4 kg

We divide this by the density

V = 2.38E4 kg / (719.7 kg/m3) = 33.1 m3

Total Cost:

We first need to convert the volume to gallons

V = 33.1 m3 * 264 gal/m3

V = 8.74E3 gal

We multiply this times the cost per gallon

C = $2.58/gal * 8.74E3 gal

C = $22,500, to 3 significant figures.

We must add this to the price of the 18-wheeler:

Total Cost = $22,500 + $98,000 = $120,500 is the total cost to the shipper

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