# A car's gas mileage is independent of the number of passengers.

## A misconception

Is the given statement true or false :- "A car's gas mileage is independent of the number of passengers".

\(\text {Why some people say it is true}\), because a vehicle drives only once to carry the passengers from one place to another, so no extra force is exerted for extra passengers.

\(\text {Why some people say it is false}\),because more the load a vehicle has to carry, more the force it has to exert.

The statement is \(\color{red} {\textbf {false}}\).

Explanation:

- A machine would give as much output as the input it receives. Similarly, a car which is a machine, would also require more input for more output i.e. to carry four passengers, it would require more fuel than what is required to carry two passengers. The force of friction is directly proportional to the normal reaction. With the increase in number of passengers, the load and hence the normal reaction increases. This results in the increase in the force of friction and hence the car consumes more fuel.

An example to make the explanation clear:Suppose the weight of one passenger is \(1200N\).The coefficient of friction between the wheel and the road is \(0.45\), then find the magnitude of limiting friction when :Thus , we see that with an increase in the number of passengers, the limiting friction increases. So, more fuel would have to be spent by the car to move more passengers , with the distance and speed remaining the same.1) There is one passenger in the car

2) There are three passengers in the car

3) There are four passengers in the car.

Case 1

Normal reaction \((N) = 1200N\)

Co-efficient of friction \(= 0.45\)

Limiting friction \((F) = \mu \times R = 0.45×1200 = 540N\)Case 2

Normal reaction \( (N) = 3600N\)

Co-efficient of friction \(= 0.45\)

Limiting friction \((F) = \mu \times N\) = \(0.45×3600 = 1620N\)Case 3

Normal reaction \((N) = 4800N\)

Co-efficient of friction = \(0.45\)

Limiting friction \( (F) = \mu \times N = 0.45×4800 = 2160N\)

Rebuttal: Once the engine gets going, due to the inertia of motion it should move in forward direction. Thus, the same amount of fuel should be used by vehicles of the same mass irrespective of the number of passengers.

Reply:A car carrying more number of passengers would directly increase the force of friction, so the magnitude of inertia of motion decreases, thus slowing down the vehicle. So, to keep up with the original speed, the car would have to consume more fuel.

**See also**

**Cite as:**A car's gas mileage is independent of the number of passengers..

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