Kinetics
Relation between work and energy
Work W performed by external forces that are acting on a body is the cause of the change of energy ΔE of the body48: W = ΔE
Let us have a look at a shot-putter, for example. He used a force of 1206 N to displace the shot by 0,5 m in the direction of the throw. The force used was constant. We will neglect vertical displacement of the shot and thus also its potential energy. Let us imagine that all work was used up to change the kinetic energy of the shot. If we know that the work of 603 J was performed, then the change of the kinetic energy of the shot in the place of throw was 603 J. What was the velocity vodhod of the shot weighing 7,26 kg at the moment of the throw?
The initial velocity of the shot at the moment of the throw was 12,88 m/s, as it follows from the relation between work and the change of kinetic energy. The increase in the mechanical energy of the shot equals only the increase in its kinetic energy, because we decided to neglect its potential energy49.
Increasing energy by performing work
In sport and physical exercise we often need to maximize kinetic energy of a given body.
In order to maximize kinetic energy of human body or sport equipment we must exert the greatest possible force along the longest possible distance.
This way we can make us of the knowledge of the relation between energy and work to improve our technique in certain sports, especially in athletics. From the relation between impulse of force and momentum we know that for better technique and thus for increasing the velocity of a projectile we need to use greatest possible force for longest possible time. According to the relation between work and energy the velocity is maximized by the greatest possible force acting along the longest possible distance.
For example shot-putters must throw the shot from a shot-put circle according to the rules, from which they must not step out. Dimensions of the shot-put circle limit the shot-putters’ possibility to perform work because they can exert force only along a limited distance. Shot-putters therefore often start their throw by standing on one foot, bent forward over the edge of the shot-put circle, with their back towards the direction of the throw, to maximize the distance along which their force will act on the shot and thus to also maximize the initial velocity of the shot at the moment of the throw (Fig. 13). The longer distance along which the force acts on the shot and the ability to use larger muscle groups thus leads to longer throws and better results.
By performing work we can increase not only kinetic but also potential energy of a body.
Figure 13 Initial phases of shot put allowing to maximize the work performed during the throw.
Decreasing energy by performing work
The relation between energy and work can also be used to explain techniques of absorbing energy of a body to prevent potential injuries of athletes. This happens mostly in catching projectiles, landing, etc. when negative work is performed. Human muscles also perform negative work when our body lands on the ground. Energy of a human body during landing is simply given and forces caused by it can lead to injuries if we don’t use the correct landing technique. During landing it is important to maximize the distance along which the projectile is decelerating. By making stopping distance longer we make impact forces smaller. We must realize, however, that prolonging the stopping distance by bending our knees deeply, for example, does not necessary lead to smaller reaction forces in specific joints. The resultant reaction force acting on the floor is smaller but for example in the knee the moment of force can even increase in comparison with landing by bending our knees less and then moving backward (Jandačka a Zahradník, 2011).
To decrease impact forces and increase stopping distance we also use various materials: sand (long jump), water (diving), running shoes, boxing gloves, etc.
Law of Conservation of Mechanical Energy
If no work is performed on a body, it follows: change of kinetic energy + change of potential energy + change of elastic energy = 0:
Total mechanical energy of a body is constant unless external forces act on it (other than gravitational force).
This law can be used in studying the motion of projectiles. For example if we assume that a pole vaulter does not perform any work after taking off, his total mechanical energy at the beginning of the vault is equal to his kinetic energy at the end of his run-up. This kinetic energy is transformed into deformation energy of the pole and subsequently into the increase in potential energy of the athlete. In other words, the faster the pole vaulter runs and the better his pole is able to transform kinetic energy into potential energy through deformation energy, the higher he jumps. Part of energy is of course transformed in other types of energy, for example internal energy of the pole, resulting in heat.
Power
In certain sports to succeed it is not enough to perform a great amount of work but we must perform a great amount of work in the shortest possible time. In mechanics such ability is described by the quantity called power50.
Average power describes the amount of work performed during a period of time. Mathematically this can be expressed as:
where P is power (W)51, W is work (J) a t is time period.
Instantaneous power is work performed over time period that is approaching zero.
Power measures speed with which work is performed.
Power can also be defined as product of average force and average velocity of displacement of a body in the direction of that force:
where P is average power (J), F is average force (N), Ft is the magnitude of the component of the average force in the direction of the body’s displacement (N), v is the magnitude of the average velocity of the body’s displacement in the direction of the average force (m/s), and v is the velocity of displacement (m/s).
Is it a good idea to swish arms when jumping up? What is the optimum gear ratio for cycling as fast as possible under the given conditions? What is the optimum length of step to walk as fast as possible under the given conditions? To answer these complicated questions it will help us to know the concept of power and also to know certain qualities of muscles.
In complex human motions the maximum output mechanical power is reached with approximately 50 % of maximum force and velocity of a given athlete (Jandačka a Vaverka, 2008). That could mean that the best gear ratio in cycling is not the top, neither the bottom, but somewhere between the both extremes. The optimum length of step in running is not the longest, neither the shortest but somewhere in between. The best choice of gear ratio, length of step, etc. is the one that allows your muscles to contract with optimum speed and optimum force, which results in maximum mechanical muscle power. In complex motor tasks the resulting power is influenced not only by qualities of individual muscles but also by muscle coordination (Wakeling, Blake a Chan, 2010).
Let us have a look again at weightlifting, specifically at the events of “clean and jerk” and “snatch”. The force with which the weightlifter acts on the barbell and the velocity of his motion indicates enormous muscle power (about 3.200 W) but only for a very short time. If the time of motion were longer, would he still be able to produce such enormous power? Duration of physical activity substantially influences the ability to produce muscle power. Sprinters are able to maintain power for a relatively short period of time (0-60 s). Power outputs of runners at medium distances are markedly lower than that of sprinters because the duration of their motor activity is increased from one to seven minutes. Marathon runners produce even lower power output because they run for two to four hours. Human metabolic system influences the ability of athletes to produce power (Fig. 14).
Figure 14 The relation between metabolic and mechanical power, and sources of energy (aerobic metabolism, anaerobic glycolysis, and high-energy phosphates) (Knuttgen a Komi, 2003).
48 For example work performed by an athelete is influenced by forces generated in interactions of the athlete’s body with its environment.Zpět
49 We also neglect air resistence and friction forces.Zpět
50 The concept of power is closely related to the concepts of fast force and explosive force, used in anthropomotorics.Zpět
51 W – unit of power is watt.Zpět