Question

how is the counter movement jump related to the ground reaction force required to jump upwards?

Answer 1

The reaction force supplied by the ground is specifically called the ground reaction force (GRF), which is basically the reaction to the force the body exerts on the ground. What is important to keep in mind is that the ground reaction force is largely under our control via coordinated muscle actions. By producing a certain combination of muscle actions, we ultimately push against the ground which pushes back against the body with an equal and opposite force. This is explained by Newton's 3rd law of motion which states that for every action there is an equal and opposite reaction.

The basic mechanical principle to be studied in this exercise is Newton's 2^nd law of motion:

where ΣF represents the summation of all forces acting on a body (i.e., the net force), m is the body's mass, and a is the acceleration of the body's center of gravity (CG). A simple model of the body illustrates the application of Newton's 2^nd law to the vertical motion of an individual during a vertical jump:

where, GRF_vis the vertical component of the ground reaction force, W is the person's body weight, is the person's body mass, a is the vertical acceleration of the CG. Therefore, from Newton's 2^nd law, we can see that if the upward push of the ground is equal to the earth's downward attraction (i.e., weight), the net force on the body equals zero and the resulting acceleration is zero. If the ground reaction force is greater than body weight, there is a net positive force acting on the body and the acceleration is positive. Finally, if the ground reaction force is less than body weight, the net force on the body is negative and the acceleration is negative.