The formulas to calculate the Work Done (W) and Maximum Force (Fmax) are:
\[ \text{W} = \frac{1}{2} k s^2 \]
\[ \text{F}_{\text{max}} = k s \]
Where:
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 was 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.
Let's assume the following values:
Using the formulas to calculate the Work Done (W) and Maximum Force (Fmax):
\[ \text{W} = \frac{1}{2} \times 500 \times (0.2)^2 = 10 \text{ J} \]
\[ \text{F}_{\text{max}} = 500 \times 0.2 = 100 \text{ N} \]
The Work Done is 10 Joules and the Maximum Force is 100 Newtons.
