Question

The fuel tank on a sport-utility wagon holds 19 gal of gasoline (p=1.32 slug /ft^3). How much heavier is the automobile when the tank is full compared to when it is empty? (Express your answer using four significant figures.) w= --- lb

Answer 1

We are asked to determine the mass of 19 gallons of gasoline. To do that we will use the following formula:

`m=\rho V`

Where:

`\begin{gathered} m=\text{ mass} \\ \rho=\text{ density} \\ V=\text{ Volume} \end{gathered}`

First, we will convert the slug to pounds using the following conversion factor:

`1\text{ slug }=32.174\text{ pounds}`

Multiplying by the conversion factor we get:

`1.32(slug)/(ft^3)*(32.174lb)/(1slug)=42.47(lb)/(ft^3)`

Now, we will convert the gallons into cubic feet using the following conversion factor:

`1\text{ gal}=1.161ft{}^3`

Multiplying by the conversion factor:

`19gal*(1.161ft^3)/(1gal)=22.06ft^3`

Now, we substitute in the formula for the mass:

`m=(42.47(lb)/(ft^3))(22.06ft^3)`

Solving the operations:

`m=936.8882lb`

Therefore, the mass is 936.8882 pounds.