Determine the amount of gasoline required in Example 4.7 if the automobile was traveling at 55. miles per hour.

Example 4.7

A gallon of gasoline can provide about 1.30 × 10⁵ kJ of chemical energy. Based on Example 4.1, if all the chemical energy of a gallon of gasoline could be converted into the translational kinetic energy of an automobile, how many gallons of gasoline would be equivalent to the vehicle’s TKE if the automobile is traveling at 65. miles per hour on a level highway?

Need: Gallons of gasoline to propel the automobile at 65. mph (29.0 m/s).

Know: TKE of vehicle = 4.2 × 10² kJ to 2 sig. figs. at 65. mph (as per our previous calculation in Example 4.1).

Energy content of gasoline is 1.30 × 10⁵ kJ/gallon.

How: Set TKE of vehicle equal to chemical energy in fuel. Let x = number of gallons needed to accomplish this.

Solve: x × 1.30 × 10⁵ [gallons][kJ/gallon] = 4.2 × 10² [kJ]. Therefore x = 0.0032 gallons.