# Eccentric force and acceleration relationship

### BBC - GCSE Bitesize: Forces, mass and acceleration

An 85kg man performed both normal speed (3 sec eccentric action and maximal acceleration concentric action) and PS back squats over a. Force = Mass x Acceleration; Acceleration = Force ÷ Mass The time of flight of the shot can be determined from the equation: the body's centre of gravity is called an eccentric force and results in movement and rotation. For a constant mass, force equals mass times acceleration. F and a in the equation indicate that force and acceleration are vector quantities.

Key points As velocity approaches zero, propulsive force approaches zero, therefore slow moving objects only require force approximately equal to the weight of the resistance.

### Centripetal force - Wikipedia

As mass is constant during resistance training, a greater impulse will result in a greater velocity. The inferior propulsive forces accompanying purposefully slow training suggest other methods of resistance training have a greater potential for adaptation.

Impulse, momentum, purposefully slow, time-under-tension Introduction Performing exercise under any type of resistance is broadly defined as resistance training Newton, Because the effect of the earth's gravity is universally present on earth, the physics of resistance training with a constant load isoinertial are relatively simple.

What are not simple, however, are the ultimate physiological and morphological effects of resistance training. Several variables can be manipulated in resistance training programs to bring about a specific desired result Wernbom et al.

Load, number of sets, number of repetitions per set, number of exercises, mode machine or free weightrepetition speed, rest period length, exercise order, training frequency, and the specific exercises selected can all be manipulated to promote a precise desired outcome.

### Force velocity relationship | S&C Research

Such outcomes include increased muscular endurance, muscle size, increased muscle strength, increased muscle power, and decreased relative body fat. It is unlikely that a single program or method will be effective in realizing all of the possible benefits of resistance training equally. Much of the support for such programs exists only in lay media Brzycki, ; Hutchins, ; Wescott,with little empirical evidence Greer, It is the purpose of this paper to correctly describe the mechanical aspects of such training, as these programs have been used in several empirical studies Greer, We will also provide a case example where the mechanical properties of a common resistance training exercise will be shown.

Specific training studies will not be reviewed in detail as they are primarily interested in physiological effects for such a review see Greer,but we hope that this mechanical review will lay the groundwork for productive evaluation of resistance training over the load and velocity spectrum.

Essentially, the F-V relationship is a hyperbolic curve constructed from the results of numerous experiments describing the dependence of force on the velocity of movement Hill, This relationship has been examined in vitro, in situ, and in vivo. The F-V relationship assumes that at a given velocity, the muscles are generating the maximum force possible. A similar load-velocity relationship is also demonstrated in isoinertial, in vivo exercise with maximal voluntary acceleration Cronin et al.

In this case, as the external load i.

The load-velocity relationship assumes that the movement velocity is the maximum possible for the given load. This relationship between force and velocity is what may have prompted some to suggest that the voluntary muscle action should be carried out over a s period so that the velocity is low, thereby increasing force Wescott, Impulse and momentum The relationship between force and velocity for a constant mass such as is encountered in free-weight training is given in the relationship between impulse and momentum.

A constant mass under the influence of a force can be expressed with Newton's second law represented by equation 1. In the above case, the acceleration a experienced by an object is directly proportional to the force impressed F and inversely proportional to its mass m. Since acceleration is the first derivative d of velocity with respect to time, the equation can also be written to reflect the first derivative with respect to time rate of change in the quantity mv. In such a case linear momentum L is expressed as equation 2.

When a force acts upon the object from a time period from t1 to t2, equation 1 can be integrated in time to obtain equation 3.

Equation 3 defines linear impulse Iand is equal to the change in linear momentum, as shown in equation 4. As mass is constant during free-weight resistance training, a greater impulse will result in a greater velocity.

In human movement, force is required first to maintain static equilibrium and second to generate acceleration. The force required to maintain static equilibrium is equal to an object's mass multiplied by gravitational acceleration. Additional force results in acceleration of a mass or a change in momentum. These components of acceleration are described in equation 5: Therefore, as generation of force greater than the weight of the resistance increases i.

As velocity approaches zero, propulsive force approaches zero, therefore slow moving objects only require force approximately equal to the weight of the resistance. The slower the intended velocity, the closer the force expressed comes to equalling the linear inertia of the load i.

From Equation 1force is inversely proportional to time. That is, to perform a movement in a shorter period of time, greater force must be generated. Arguments have been made that the muscle tension will be constant through the given range of motion, and thus provide optimum stimulation throughout such range Wescott, This statement has not been experimentally verified and unfortunately neglects the changes in moment arm and muscle length which ultimately change the muscle force regardless of speed of action.

This argument does, however, have some factual basis, as the impulse increases as time increases Equation 4in the case of maximal effort actions. In the case of PS, increasing time decreases force, and excessive time duration will not maximize impulse. Arguments for purposefully slow PS training Muscle force: While PS proponents vary in their reasoning for suggesting this method, the basic premise is that when the weight is moving quickly, the muscles will not be able to exert as much force and thus the training effect will be diminished Brzycki, ; Wescott, Acta Physiologica Scandinavica, 2 Intended rather than actual movement velocity determines velocity-specific training response.

Journal of Applied Physiology, 74 1 Journal of Sports Sciences, 7 3 Why is the force-velocity relationship in leg press tasks quasi-linear rather than hyperbolic?. Journal of Applied Physiology, 12 Training-induced alterations of the in vivo force-velocity relationship of human muscle.

Journal of Applied Physiology, 51 3 Specificity of power improvements through slow and fast isokinetic training. Journal of Applied Physiology, 51 6 Force—velocity relationship of leg extensors obtained from loaded and unloaded vertical jumps.

European Journal of Applied Physiology, 8 Force-velocity relationship on a cycle ergometer and knee-extensor strength indices. Canadian Journal of Applied Physiology, 27 3 Effects of velocity of isokinetic training on strength, power, and quadriceps muscle fibre characteristics.

The effects of eccentric and concentric training at different velocities on muscle hypertrophy.

• Forces, mass and acceleration
• Don’t Confuse The Force-Velocity Curve With Newton’s Second Law
• Biomechanics

European Journal of Applied Physiology, 89 6 Muscular force at different speeds of shortening. The Journal of Physiology, 85 3 A comparison of the kinematics, kinetics and muscle activity between pneumatic and free weight resistance.

## Newton's Second Law

European Journal of Applied Physiology, 6 Journal of Applied Biomechanics. Interdependence of torque, joint angle, angular velocity and muscle action during human multi-joint leg extension. Muscle fascicle shortening behaviour of vastus lateralis during a maximal force—velocity test. European Journal of Applied Physiology, The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society of London B: Biological Sciences, Role of concentric force in limiting improvement in muscular strength.

Journal of Applied Physiology, 68 2 Effects of load and contraction velocity during three-week biceps curls training on isometric and isokinetic performance.

International Journal of Sports Medicine.

ForceVelocity

Comparison of treadmill and cycle ergometer measurements of force-velocity relationships and power output. International Journal of Sports Medicine, 20 3 Effect of countermovement on power—force—velocity profile.