How to Calculate the Force Needed to Move a Car

by Matthew R. JorgensenKnowing the force required to move a car is essential in the engineering of the automobile or any other transportation device - from railroad cars to the space shuttle. Thankfully, there are simple physical laws that govern this type of motion which are universally applicable. This article explains Newton's second law as it relates to the acceleration of an automobile.

### Use Newton's Second Law

Use Newton's second law which states that whenever two or more objects interact with each other there is a force acting on them. There are two general types of forces: contact forces (applied force, friction and others) and at-a-distance or field forces (gravity, electrical and magnetic).

Focus on the applied force to the car. If the car is on flat ground and friction is negligible (which is true if it has inflated tires and is moving slowly), then the force required to accelerate the car is given by force = mass times acceleration or F=M x a. According to this, even a very small amount of force is sufficient to move a car, albeit slowly.

Using the mass "M" of the automobile in question in kilograms (1 Kg = 2.2 pounds) and the acceleration "a" desired in meters per second squared, insert the parameters into Newton's second law equation to get the force "F" required in kilogram meters per second squared, which is equivalent to the basic unit of force, the Newton.

### If the Car is on an Incline

Consider the perpendicular component of the downward force in addition to the force required to accelerate.

Calculate the downward force caused by gravity by multiplying the car's mass in kilograms by the standard gravity acceleration constant, 9.8 meters per second squared.

Calculate the perpendicular component of this force by multiplying it by the cosine of 90 degrees minus the incline, which may also be called theta, as is shown in the picture (down force x cos(90-incline) = down force x cos(theta) = perpendicular component of force).

For example: the orange Jeep shown above weighs 3,200 pounds (1,450 Kg), and is sitting on a 30 degree incline. The force from gravity acting on the Jeep in the direction it can roll (the perpendicular component of the force) is the downward force (9.8 x 1,450 = 14,250 Newtons) times the cosine of 90 minus the incline (cos(90-30) = 0.5) which is 14,250 x 0.5 = 7,125 Newtons.

This means, according to Newton's second law, that if the Jeep was free to roll it would accelerate down the slope at 7,125 Newtons divided by 1,450 Kg which is equal to 5 meters per second squared. After one second of rolling, the Jeep would be moving 5 meters per second or 11 miles per hour.

#### Tip

- Check to make sure you are using standard scientific units: kilograms, meters, seconds and newtons. Use common sense when working with inclines. If the car is tilted downward, it is going to want to roll that way.

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#### Photo Credits

- Photo by Matthew Jorgensen