Kinetics
Law of Conservation of Momentum
In biomechanics momentum p is the product of mass of a human body m (or mass of any object) and its velocity v:
p = mv33
Momentum allows us to use a single value to express the measure of both motion and inertia of the given body. In sport and physical exercise most bodies have constant mass. If their velocity does not change, their momentum also stays constant. We know that velocity does not change if the following holds true: ΣF = o34. Therefore we can state: 
if the resultant force acting on a body is zero. Since velocity is a vector, momentum is also a vector quantity. Law of Conservation of Momentum is not very interesting when applied to a single body but it becomes very important to us when applied to behaviour of two and more bodies.
The analysis of motion of several bodies will be simpler if we imagine that each body is a part of one system on which no external forces act because the vector sum of all external forces acting on that system is zero.
If no external force acts on a closed system of bodies, the momentum of the closed system remains constant.
35
thus
Law of Conservation of Momentum can be specifically applied to the analysis of collisions in sport and physical exercise. Collisions in sport and physical exercise can be found everywhere – in boxing, kicking the ball, body checking in ice hockey, etc. Results of such collisions can be explained using Law of Conservation of Momentum.
Elastic collisions
If two bodies encounter in a totally elastic collision36, their resultant total momentum is conserved. Moreover, in this case the Law of Conservation of Energy is not infringed due to deformation of the bodies. This principle can be used to predict the resultant velocities of both bodies after the collision:
v1 and v2, respectively, are velocities of the bodies before the collision, u1 and u2, respectively, are velocities of the bodies after the collision, m1 a m2 are masses of the bodies that encountered in the collision.
In elastic collision the bodies are pressed for a very short time and their kinetic energy is conserved in them as deformation energy (similarly to a compressed spring). This energy is rapidly transformed back to kinetic energy and used in a totally elastic collision for rebound, with no residuum. In elastic collision part of kinetic energy is transformed into heat (i.e. vibration energy of the atoms).
There are three types of collisions that can be described by the model of totally elastic collision:
- A moving body encounters a static body, acting with a central force37 (For example a pool ball hits a static ball and stops, while the originally static ball takes over its velocity.) Generally speaking (balls with various masses) the moving ball gives all its momentum to the static ball.
- Two bodies encounter with opposite velocities and exchange their momenta.
- The first body is faster than the second body and both bodies move before encounter in the same direction. Again, they exchange their momenta. Such situation occurs when a faster cross country skier in a downhill section catches up a slower skier and by touching him passes on him his momentum. At the same time the faster skier receives momentum from the skier ahead of him38.
Inelastic collisions
Not all collisions are elastic. In totally inelastic collisions momentum is also conserved but after the collision both bodies move together in the same resultant direction. The following then holds true:
where u is resultant common velocity. Most collisions in rugby are almost totally inelastic. Both players move in the same direction after the collision. Can a faster but lighter player be more successful in a collision than a heavier but slower player?
Let us imagine a situation of a defender with the weight of 80 kg colliding with a forward weighing 120 kg. Just before the collision the defender’s velocity is 6 m/s while the forward’s velocity is -5 m/s (opposite direction). Will the forward move ahead and score or will he be stopped?
The forward will move ahead in the original direction of his motion with the velocity of 0,6 m/s together with the defender and probably score.
Most collisions in sport are neither totally elastic, nor totally inelastic.
33 In English literature linear momentum is sometimes denoted with capital L.Zpět
34 Where o is zero vector.Zpět
35 Where o is zero vector.Zpět
36 A totally elastic collision exists only in theory. It is a model that simplifies the reality. But certain collisions have qualities that are very close to that model.Zpět
37 Concept of central force is explained in the chapter: Moment of force: Causes of rotary motion and keeping the balance.Zpět
38 Inelastic deformations of humand body and motions in joints are neglected.Zpět