Calculating the Force of Impact

During an impact, the energy of a moving object is converted into work, and force plays an important role. To create an equation for the force of any impact, you can set the equations for energy and work equal to each other and solve for force. From there, calculating the force of an impact is relatively easy.

TL;DR (Too Long; Didn’t Read)

To calculate the force of impact, divide kinetic energy by distance.

Impact and Energy

Energy is defined as the ability to do work. During an impact, an object’s energy is converted into work. The energy of a moving object is called kinetic energy, and is equal to one half of the object’s mass times the square of its velocity:

(KE=frac{1]{2}mv^2)

When thinking about the impact force of a falling object, you can calculate the energy of the object at its point of impact if you know the height from which it was dropped. This type of energy is known as gravitational potential energy and it is equal to the object’s mass multiplied by the height from which it was dropped and the acceleration due to gravity:

(PE=mgh)

Impact and Work

Work occurs when a force is applied to move an object a certain distance. Therefore, work is equal to force multiplied by distance:

(W=Fd)

Because force is a component of work and an impact is the conversion of energy into work, you can use the equations for energy and work to solve for the force of an impact. The distance traveled when the work is accomplished by an impact is called the stop distance. It is the distance traveled by the moving object after the impact has occurred.

Impact From a Falling Object

Suppose you want to know the impact force of a rock with a mass of one kilogram that falls from a height of two meters and embeds itself two centimeters deep inside of a plastic toy. The first step is to set the equations for gravitational potential energy and work equal to each other and solve for force.

(W=PE=Fd=mgh implies F=frac{mgh}{d})

The second and final step is to plug the values from the problem into the equation for force. Remember to use meters, not centimeters, for all distances. The stop distance of two centimeters must be expressed as two hundredths of a meter. Also, the acceleration due to gravity on Earth is always 9.8 meters per second per second. The force of impact from the rock will be:

(F=frac{(1)(9.8)(2)}{0.02}=980text{ N})

Impact From a Horizontally Moving Object

Now suppose you want to know the impact force of a 2,200-kilogram car traveling at 20 meters per second that crashes into a wall during a safety test. The stop distance in this example is the crumple zone of the car, or the distance by which the car shortens on impact. Suppose the car is squished enough to be three quarters of a meter shorter than it was before the impact. Again, the first step is to set the equations for energy — this time kinetic energy — and work equal to each other and solve for force.

(W=KE=Fd=frac{1}{2}mv^2 implies F = frac{1/2 mv^2}{d})

The final step is to plug the values from the problem into the equation for force:

(F = frac{1/2 (2,200)(20)^2}{0.75}=586,667 text{ N})