The feet of a standing person of mass m exert a force equal to mg on the floor, and the floor exerts an equal and opposite force upwards on the feet, which we call the normal force. During the extension phase of a vertical jump, the feet exert a force on the floor that is greater than mg, so the normal force is greater than mg. We can use this result and Newton's second law to calculate the acceleration of the jumper: a = Fnet / m = (n - mg)/ m.
Using energy ideas, we know that work is performed on the jumper to give him or her kinetic energy. But the normal force can't perform any work here because the feet don't undergo any displacement. How is energy transferred to the jumper?
The jumper is not a rigid body.
The problem discussed the "extension phase".
During that phase the force is moving the center of mass of the jumper up (not the feet but somewhere around the belly button), thereby creating a force times the displacement of the CG of the person.
(It is hard to jump up without crouching down first :)
During the extension phase of a vertical jump, the energy is transferred to the jumper through the contraction and subsequent release of muscles. The muscles in the legs contract, storing potential energy in a compressed form. When the muscles are released, this potential energy is converted into kinetic energy, propelling the jumper upwards.
The normal force, exerted by the floor on the feet, plays a crucial role in this energy transfer. Although the normal force does not perform work in the traditional sense (since there is no displacement), it enables the muscles to exert a force greater than the weight (mg) on the floor. This allows for the acceleration of the jumper and the conversion of potential energy to kinetic energy.
So, while the normal force may not directly transfer energy to the jumper, it is a crucial factor in enabling the transfer of energy through muscle contraction and the resulting acceleration during a vertical jump.
Energy is transferred to the jumper during a vertical jump through the process of muscle contraction. When a person jumps, the muscles in their legs and feet contract, generating a force that allows them to push off the ground. This force does work on the person, transferring energy to their body.
During the extension phase of a vertical jump, the force exerted by the feet on the floor is greater than the person's weight (mg). This additional force enables the person to push against the floor with more strength, resulting in a greater acceleration and height in the jump.
However, it's important to note that the normal force itself does not directly transfer energy to the jumper. The normal force is simply a reaction force exerted by the floor on the person's feet to counteract their weight. It does not perform any work because, as you mentioned, the feet don't undergo any displacement.
Instead, the energy required for the jump comes from the chemical energy stored in the muscles. When a person jumps, their leg muscles contract, converting chemical energy into kinetic energy as they push against the ground. This transferred energy allows the person to gain velocity and, ultimately, kinetic energy.
In summary, energy is transferred to a jumper during a vertical jump through the contraction of their muscles, which converts chemical energy into kinetic energy. The normal force does not directly transfer energy but rather ensures that there is an upward reaction force to support the person's weight.