A 3000-kg truck needs a propeling steady force of 1400 N to travel at a speed of 40 mpg. What is the MPG for the truck if its engine efficiency is 27%? Heat released from one gallon=136,500,000 J and 1 m= 1609 m.

To find the miles per gallon (MPG) for the truck, we need to calculate the distance (in miles) the truck can travel with one gallon of fuel.

First, let's calculate the work done by the truck's engine to overcome the resistance and propel the truck. We can use the formula:

Work = Force × Distance

The work done by the engine is equal to the propelling force multiplied by the distance traveled. Rearranging the formula, we have:

Distance = Work / Force

Given that the truck needs a propelling force of 1400 N to travel at a speed of 40 mpg, the work done by the engine can be calculated using the formula:

Work = Force × Distance = 1400 N × 40 miles

Next, we need to calculate the energy released from one gallon of fuel. Given that the heat released from one gallon of fuel is 136,500,000 J, we have:

Energy released from one gallon = 136,500,000 J

Now, we need to consider the efficiency of the truck's engine, which is given as 27%. The engine efficiency is the ratio of the useful work output to the energy input. Rearranging the formula for efficiency, we have:

Efficiency = (Useful work output / Energy input) × 100

Since we want to find the distance traveled with one gallon of fuel, the useful work output is equal to the work done by the engine. Therefore, we can rewrite the formula as:

Efficiency = (Work / Energy input) × 100

Rearranging the formula to solve for work, we have:

Work = (Efficiency / 100) × Energy input

Substituting the given values, we have:

Work = (27 / 100) × 136,500,000 J

Now, we can substitute the calculated work value back into the formula for distance:

Distance = Work / Force = ((27 / 100) × 136,500,000 J) / 1400 N

Finally, we need to convert the distance from meters to miles. Given that 1 mile is equal to 1609 meters, we can convert the distance in meters to miles using the conversion factor 1 mile / 1609 meters:

Distance (in miles) = (Distance (in meters)) ÷ 1609

Now, we can calculate the MPG by dividing the distance (in miles) by 1 gallon:

MPG = Distance (in miles) / 1 gallon

By following these steps and performing the calculations, you should be able to determine the MPG for the truck when its engine efficiency is 27%.