Enter the total deformation distance and the spring constant of the collision to determine the impact force of an object, such as a car crash.

## Impact Force Formula

The following formula is typically used to calculate and impact force.

W = 1/2 F_{max} s = 1/2 k s^{2}

- W = work done (J, ft lb)
- F
_{max}= maximum force at the end of the deformation (N, lb_{f}) - s = deformation distance (m, ft)
- k = spring constant

## Impact Force Definition

Impact force is a term used in physics, specifically in mechanics, to describe a force of a short period of time when objects collide. A high force applied to an object in a short amount of time results in very quick acceleration. This fast acceleration is what causes much of the damage in collisions. Whether that is a car or a person’s body part.

If this force as to be applied for a long period of time, the acceleration would be much smaller and the resulting damage would be much less. As a result, things like cars are designed to increase the amount of time the force is applied. In other words, cars are meant to crumple and deform because a slower acceleration, or in the case of a car crash, deceleration, is safer for a human body to endure.

As can be seen, by the formula above, the work done is directly proportional to the spring constant and exponentially related to the deformation. For this reason, cars are meant to deform as much as possible during crashes.

## How to calculate an impact force?

The following example is a step-by-step guide on how to calculate the impact force of a collision between two cars.

- First, we must analyze the equation above to determine the missing variables and the correct formula. After re-arranging some variables, we find that the max force = k * s where k is the spring constant and s is the displacement.
- We will assume for this problem that the car is colliding with a wall that has no deformation. In this case, the deformation is equal to 1 meter.
- Next, we need to determine the spring constant. The car is clearly not a traditional spring, but a front-on collision can be studied very well to get an accurate representation of the spring constant of the car. For this example, we will assume that the data collected by the car manufacturer shows a spring constant of 10,000 N/m.
- Finally, and the information into the formula above and we find F = 10,000 N/m * 1 m = 10,000 N.
- One last final step could be to determine the resulting acceleration a human body feels during that time frame to determine the extent of injuries

## FAQ

**What is an impact force?**

Impact force is a term used in physics, specifically in mechanics, to describe a force of a short period of time when objects collide.