# Impulse and velocity relationship

### Momentum and Impulse Connection

is a vector quantity (since velocity is a vector and mass is a scalar). The impulse-momentum theorem is logically equivalent to Newton's second law of motion. What is the relation between momentum and impulse in mathematical steps? . Thus momentum is a factor of mass and velocity with which a body is travelling. Force, Momentum, and Impulse. We know how to calculate the kinetic energy of moving objects -- isn't that enough? No. It turns out that many situations.

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.

### What are momentum and impulse? (article) | Khan Academy

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.

### Impulse & Momentum - Summary – The Physics Hypertextbook

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.

**Introduction to momentum - Impacts and linear momentum - Physics - Khan Academy**

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, While true that the muscles will not produce as much force at the higher velocities during maximum effort velocity-controlled actions, the previous statement ignores the requisite force to initiate high velocity movements for a given load in an isoinertial condition.

In addition, the aforementioned F-V relationship was derived under conditions of maximal acceleration maximal voluntary muscle activationand thus differs from intentionally slow movements.

An attempt to reduce the speed of motion subsequently reduces the force expressed Keogh et al. Modifications to any one of these metabolic factors during exercise may alter signal transduction pathways and hence modify gene transcription for muscle growth Rennie et al. Potential strength adaptations due to acute metabolic stimuli have recently been reviewed elsewhere Crewther et al.

The metabolic hypothesis has not yet been examined in conjunction with PS training studies; therefore these ideas are currently speculative for this type of training. Movements performed at low velocities prolong the time of contraction in each repetition for a given range of motion time-under-tension; TUT.

Proponents of PS training regard this increased time as a positive characteristic to stimulate training adaptation Wescott et al.

## Impulse & Momentum

TUT can be considered a manner by which to prescribe a dose of resistance exercise Tran and Docherty,which is crucial as the optimal dose for weight training is subject to tremendous debate Carpinelli and Otto, ; Stone et al. The more momentum that an object has, the harder that it is to stop.

Thus, it would require a greater amount of force or a longer amount of time or both to bring such an object to a halt. As the force acts upon the object for a given amount of time, the object's velocity is changed; and hence, the object's momentum is changed.

The concepts in the above paragraph should not seem like abstract information to you. You have observed this a number of times if you have watched the sport of football. In football, the defensive players apply a force for a given amount of time to stop the momentum of the offensive player who has the ball.

You have also experienced this a multitude of times while driving. As you bring your car to a halt when approaching a stop sign or stoplight, the brakes serve to apply a force to the car for a given amount of time to change the car's momentum.

An object with momentum can be stopped if a force is applied against it for a given amount of time. A force acting for a given amount of time will change an object's momentum.

Put another way, an unbalanced force always accelerates an object - either speeding it up or slowing it down. If the force acts opposite the object's motion, it slows the object down. If a force acts in the same direction as the object's motion, then the force speeds the object up.

Either way, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is changed. Impulse These concepts are merely an outgrowth of Newton's second law as discussed in an earlier unit. To truly understand the equation, it is important to understand its meaning in words. In words, it could be said that the force times the time equals the mass times the change in velocity.

The physics of collisions are governed by the laws of momentum; and the first law that we discuss in this unit is expressed in the above equation. The equation is known as the impulse-momentum change equation.

The law can be expressed this way: