Impact Force

Impact forces acting on falling objects, crashed cars ..

crashed car

The dynamic energy in a moving object, like a falling ball or a driving car, can be expressed as

E = 1/2 m v2   (1)

where

E = dynamic energy (J, ft lb)

m = mass of the object (kg, slugs)

v = velocity of the object (m/s, ft/s)

Work made by a impact force slowing down the object can be expressed as

W = F s   (2)

where

W = work done (J, ft lb)

F = slow down force (N, lbf)

s = slow down distance (m, ft)

In an impact like a car crash the dynamic energy from the object is converted to work. The equations can be combined as

F s = 1/2 m v2   (3)

or expressed as a function of the slow down distance

F = 1/2 m v2 / s

Or to express the slow down distance

s = 1/2 m v2 / F

Note! The slow down distance is very important and a key to limit the impact forces acting in car crashes.

Example - Crashing Car

A car with a mass of 2000 kg drives in 60 km/h (16.7 m/s) before it crashes in a massive concrete wall. The front of the car impacts 0.5 m (slow down distance). The impacting force can be calculated as

F = 1/2 (2000 kg) (16.7 m/s)2 / (0.5 m) 

   = 558 kN

Note that the gravitation force acting on the car is

Fw = m g

  = (2000 kg) (9.81 m/s2)

  = 19.6 kN

Impact Force from a Falling Object

The dynamic energy in a falling object at the impact moment can be expressed as

E = Fw h

   = m g h  (4)

where

Fw = force due to gravity - weight (N, lbf)

g = acceleration of gravitity (9.81 m/s2, 32.17405 ft/s2)

h = falling height (m)

The equation can be combined with the equation of work:

F = m g h / s   (5)

Example - a Falling Car

The same car as above falls from a height of 14.2 m and crashes with the front down on a massive concrete tarmac. The front impacts 0.5 m (slow down distance) as above. The impact force can be calculated as

F = (2000 kg) (9.81 m/s2) (14.2 m) / (0.5 m)

   = 557 kN

Note! - a car crash in 90 km/h (25 m/s) compares to a fall from a height of 32 m!

Example - a Person falling from a Table

A person with weight (gravitational force) of 200 lbs (lbf) falls from a 4 feet high table.

The energy of the falling body when it hits the ground can be calculated using (4) as

E = (200 lbf) (4 ft)

   = 800 ft lb

The impact on a human body can be difficult to determine since it depends on how the body hits the ground - which part of the body, the angle of the body and/or if hands are used to protect the body and so on. 

For this example we use an impact distance of 3/4 inch (0.0625 ft) to calculate the impact force:

F = (800 ft lb) / (0.0625 ft)

  = 12800 lbf

Related Topics

  • Dynamics - Dynamics Motion - velocity and acceleration

Related Documents

  • Force - Force, Newton's third Law and acceleration

Tag Search

  • en: impact force energy work acceleration
  • es: fuerza de impacto aceleraci√≥n trabajo de energ√≠a
  • de: Schlagkraft Energiearbeit Beschleunigung

Search the Engineering ToolBox

- "Search is the most efficient way to navigate the Engineering ToolBox!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro. Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!

close