# Impact Force

## Impact forces acts on falling objects hitting ground, crashing cars and similar

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)

The work made by an impact force slowing down the moving 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 to

F s = 1/2 m v2                (3)

- expressed as slow down force

F = 1/2 m v2 / s

- expressed as slow down distance

s = 1/2 m v2 / F

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

### Example - Crashing Car

A car with a mass of 2000 kg drives in speed 60 km/h (16.7 m/s) before it crashes in a massive concrete wall. The front of the car impacts 0.5 m (the slow down distance). The impact 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 only

Fw = m g

= (2000 kg) (9.81 m/s2)

= 19.6 kN

The impact creates a force 28 times the gravity!!

### Impact Force from a Falling Object

The dynamic energy in a falling object at the impact moment when it hits the ground can be calculated as

E = Fw h

= m ag h              (4)

where

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

ag = acceleration of gravity (9.81 m/s2, 32.17405 ft/s2)

h = falling height (m)

The equation can be combined with the equation of work to:

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 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 - Motion - velocity and acceleration, forces and torques

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