# Impact Force

## Impact forces acting on falling objects, crashed cars ..

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

*E = 1/2 m v ^{2} (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, lb _{f})*

*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 v ^{2} (3)*

or expressed as a function of the slow down distance

*F = 1/2 m v ^{2 }/ s*

Or to express the slow down distance

*s = 1/2 m v ^{2 }/ 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

*F _{w} = m g *

* = (2000 kg) (9.81 m/s ^{2})*

* = 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 = F _{w} h*

* = m g h (4)*

*where *

*F _{w} = force due to gravity - weight (N, lb_{f})*

*g = acceleration of gravitity (9.81 m/s ^{2}, 32.17405 ft/s^{2})*

*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/s ^{2}) (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 (lb _{f})* 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 lb _{f}) (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 lb _{f}*

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