Final answer:
To determine the force needed to keep a car moving at a constant speed against friction and estimate the gasoline consumption at various speeds, we use work-energy principles. The efficiency of gasoline in performing useful work is considered, and the force is found to be directly proportional to speed for given distance traveled. Therefore, the given statement is TRUE.
Step-by-step explanation:
Car Movement and Gasoline Efficiency
When a car is moving on a straight road at a constant speed in one direction, the net force on the car is zero. If a car travels 108 km at a speed of 30.0 m/s (which is equivalent to 108 km/h) and uses 2.0 gal of gasoline, it implies a specific fuel efficiency. Given that only 30% of the gasoline's energy goes into useful work to counteract friction and keep the car moving at constant speed, we can calculate the magnitude of the force exerted to maintain this speed. The energy content of gasoline is approximately 140 MJ/gal, and this energy is used to perform work against frictional forces over the distance traveled.
To find the force exerted, we use the formula: work = force × distance. Since only 30% of the energy is used for work, we calculate the work performed with 0.3 × 140 MJ for 2 gallons. Once we have the work, we can find the force by rearranging the formula. If we consider that the required force is directly proportional to speed, we can predict the gasoline consumption for different speeds, such as for a speed of 28.0 m/s for the same distance traveled.
For example:
- Calculate the work done using the energy content of gasoline: Work = 0.3 × 2 gal × 140 MJ/gal.
- Convert the distance into meters: Distance = 108 km = 108,000 m.
- Find the force using the work-energy principle: Force = Work / Distance.
- Adjust for different velocities if required, using the proportional relationship between force and speed.
The number of gallons of gasoline necessary for different speeds can then be estimated based on the proportional change in force.