how many kilometers per liter will a car obtain if its engine is 25% efficient and it encounters an average retarding force of 500N at highway speed? assume that the energy content of gasoline is 40Mj/liter

The work required to move the car 1 km will be 500 N x 1000 m = 5*10^5 J

At 25% efficiency, 20*10^5 J (=2 MJ) of chemical (fuel) energy will be required.

That will require 1/20 of a liter of gas, since you get 40 MJ of energy per lier.

The gas mileage is the reciprocal of that, 20 km per liter.

Well, let's do some clown math, shall we? If the car's engine is 25% efficient, that means it is converting only a quarter of the energy from gasoline into useful work. So, out of 40 MJ of energy in one liter of gasoline, we can expect the engine to use only 10 MJ for work.

Now, let's take a closer look at the retarding force of 500 N. Imagine the car trying to move forward, but this force is constantly pulling it back. That's like trying to walk with an angry circus clown hanging onto your leg. It's not easy!

To calculate the distance the car can travel, we need to know the force acting against it. In this case, that's 500 N. Since work is force multiplied by distance, we divide the work done (10 MJ) by the force (500 N) to find the distance.

10 MJ / 500 N = 20,000,000 J / 500 N = 40,000 J/N

So, the car can move 40,000 meters (or 40 kilometers) with each liter of gasoline. Keep in mind, though, that this number represents ideal conditions and does not account for other factors like air resistance, hills, or clowns stealing your wheels.

To find out the kilometers per liter that a car will obtain, we need to calculate the energy consumed per kilometer by the car's engine.

Step 1: Calculate the power required to overcome the retarding force:
Since the retarding force is given as 500N, and the car is traveling at highway speed, we assume that the retarding force is constant. The power required to overcome the retarding force can be calculated using the equation:
Power = Force x Velocity

In this case, the velocity is the speed at which the car is traveling on the highway.

Step 2: Calculate the efficiency of the car's engine:
Given that the engine is 25% efficient, we can say that the engine converts only 25% of the energy it consumes into useful work. So, the effective power output of the engine can be calculated by multiplying the power required to overcome the retarding force by 0.25 (25%).

Step 3: Calculate the energy consumed per kilometer:
The energy consumed per kilometer is the effective power output of the engine divided by the car's speed. This will give us the energy consumed in joules per kilometer.

Step 4: Convert the energy consumed per kilometer from joules to megajoules:
The energy content of gasoline is given in megajoules per liter, so we need to convert the energy consumed per kilometer from joules to megajoules.

Step 5: Calculate the kilometers per liter:
Finally, we can calculate the kilometers per liter by dividing the energy content of gasoline (in megajoules per liter) by the energy consumed per kilometer (in megajoules).

Let's plug in the values and calculate each step:

Step 1: Calculate the power required to overcome the retarding force:
Power = Force x Velocity
Assuming the velocity of the car is given, please provide the value.

To calculate the kilometers per liter (km/L) that the car will obtain, we need to consider the efficiency of the engine and the retarding force acting on the car.

First, let's determine the work done by the retarding force. The work done by a force is given by the formula:

Work = Force x Distance

In this case, the retarding force is acting against the motion of the car, so the distance we're interested in is the distance over which the car moves while experiencing this force. Since we are assuming the car is traveling at highway speed, we can consider a reasonable average speed for this calculation.

Let's assume the car travels at a constant speed of 100 km/h (which is approximately highway speed). With this information, we can calculate the distance covered by the car in one hour:

Distance = Speed x Time
Distance = 100 km/h x 1 h = 100 km

Now, let's determine the work done by the retarding force. We can use the equation:

Work = Force x Distance

Given that the retarding force is 500N and the distance is 100 km (100,000 meters), we can calculate the work done:

Work = 500 N x 100,000 m = 50,000,000 Nm = 50,000,000 J (Joules)

Next, we need to find the energy content consumed by the engine to overcome this retarding force. Since the engine is 25% efficient, we can calculate the amount of energy consumed:

Energy consumed = Work done / Efficiency

Energy consumed = 50,000,000 J / 0.25 = 200,000,000 J (Joules)

Now, let's convert the energy consumed to Megajoules (MJ), using the energy content of gasoline, which is given as 40 MJ/L:

Energy consumed in liters = Energy consumed / Energy content per liter

Energy consumed in liters = 200,000,000 J / 40 MJ = 5 liters

Finally, we can determine the kilometers per liter (km/L) obtained by the car:

Kilometers per liter = Distance traveled / Fuel consumed

Kilometers per liter = 100 km / 5 liters = 20 km/L

Therefore, the car will obtain approximately 20 kilometers per liter.

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