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)


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)


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)


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

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