# Coercive force

As coercive force is known in classical mechanics that force that causes a body of a by predetermined constraints can not move out prescribed range.

An external force that is not a constraining force is also referred to as an impressed force for purposes of distinction . The total force acting on the body is the sum of the applied force and constraining force. The distinguishing feature is that an impressed force is physically specified according to size and direction (e.g. weight force, wind pressure, Coulomb sliding friction forces), while the constraining force is created according to size and direction depending on the specific sequence of the movement, as it is necessary for the Body follows the given restriction of its freedom of movement (e.g. by rigid guidance ).

Constraint forces have in common with the forces caused by constraint that external movement restrictions are responsible for the development and that they vary in size (in the first case depending on the movement of the body in question, in the second case depending on the environmental conditions). Compared to the constraining forces, however, the constraint is a term of statics . The internal stresses of the components caused by the constraint are relevant there with a view to their strength .

## Examples

The constraining force ( centripetal force ) exerted on a racing car by the rail keeps it on track. It is at right angles to the direction of movement.
• Gravity acts as an impressed force on a block that is standing on a flat surface . Since the block obviously rests and does not move in the direction of the center of the earth, the surface exerts a constraining force on it which is opposite to gravity and which precisely compensates for it. (How this force physically comes about is irrelevant for the consideration in the context of classical mechanics; here the secondary condition is sufficient that the block does not dip into the surface .)
• The sled of a roller coaster is held on its track by constraining forces exerted by the rails .
• A constraining force acts along the thread on a pendulum body that hangs on a thread.

## General properties

If a body can only move (freely) on a curve or a surface, the constraining force is always perpendicular to this and thus also to the direction of movement. It follows from this, among other things, that constraining forces cannot do any work , except when the curve or surface itself moves, so that the constraints explicitly depend on time.

The d'Alembert principle for setting up equations of motion is based on the proposition that the virtual work of the constraining forces vanishes; when Jourdainschen principle is exploited that the virtual power of the constraining forces disappears.

## literature

• Friedhelm Kuypers: Classic mechanics . 8th edition. Wiley-VCH, Weinheim 2008, ISBN 978-3-527-40721-7 .
• Dietrich Stauffer: Theoretical Physics . 2nd Edition. Springer, Berlin 1996, ISBN 3-540-56604-X .
• Dietmar Gross, Werner Hauger, Jörg Schröder, Wolfgang A. Wall: Technical Mechanics 1 - Statics . 11th edition. Springer, 2011, ISBN 978-3-540-68394-0 .

## Individual evidence

1. Jarg Schrader: Statik . Springer, 2004, ISBN 3-540-22166-2 , pp. 8-9.
2. ^ Horst Czichos, Manfred Hennecke: Hut: the engineering knowledge . Springer, 2004, ISBN 3-540-20325-7 , p. E17.