How can impulse be increased

In many sports the elementary motor task is to change as much as possible the velocity of human body, its parts, or of an object. In throwing, kicking, tossing, and jumping the projectiles at the beginning of their motion have zero velocity.

When fulfilling a motor task, for example throwing javelin, we are trying to give the javelin at the end of our motion the greatest possible velocity. We are therefore trying to increase the momentum of the javelin.

The same follows for certain strokes in tennis, boxing and other sports. The important thing is that to change momentum we have to either use greater force or increase the duration of the same force. The greater the impulse of force, the greater the change to momentum of a body projectile, human body, tennis racket, ball, etc. When throwing light objects, the technique used duration of force is much more important for the longest possible throw than the magnitude of the force.

When throwing heavy objects, the magnitude of the force is more important. Shot-putters are usually stronger and bigger than javelin throwers. Suppose you apply a force on a free object for some amount of time. Alternatively, the more time you spend applying this force, again the larger the change of momentum will be, as depicted in Figure.

Figure 9. If a force is exerted on the lower ball for twice as long as on the upper ball, then the change in the momentum of the lower ball is twice that of the upper ball. Mathematically, if a quantity is proportional to two or more things, then it is proportional to the product of those things. The resulting impulse on the object is defined as. However, a result from calculus is useful here: Recall that the average value of a function over some interval is calculated by.

Applying this to the time-dependent force function, we obtain. Therefore, from Figure ,. In fact, though, the process is usually reversed: You determine the impulse by measurement or calculation and then calculate the average force that caused that impulse. Note that the integral form, Figure , applies to constant forces as well; in that case, since the force is independent of time, it comes out of the integral, which can then be trivially evaluated. Approximately 50, years ago, a large radius of 25 m iron-nickel meteorite collided with Earth at an estimated speed of [latex] 1.

The impact produced a crater that is still visible today Figure ; it is approximately m three-quarters of a mile in diameter, m deep, and has a rim that rises 45 m above the surrounding desert plain. Use impulse considerations to estimate the average force and the maximum force that the meteor applied to Earth during the impact.

It is conceptually easier to reverse the question and calculate the force that Earth applied on the meteor in order to stop it. Using the given data about the meteor, and making reasonable guesses about the shape of the meteor and impact time, we first calculate the impulse using Figure.

We then use the relationship between force and impulse Figure to estimate the average force during impact. Next, we choose a reasonable force function for the impact event, calculate the average value of that function Figure , and set the resulting expression equal to the calculated average force.

This enables us to solve for the maximum force. For simplicity, assume the meteor is traveling vertically downward prior to impact. The problem says the velocity at impact was [latex] Substituting these values gives.

This is the average force applied during the collision. Next, we calculate the maximum force. The impulse is related to the force function by. We need to make a reasonable choice for the force as a function of time. Then we assume the force is a maximum at impact, and rapidly drops to zero. A function that does this is.

The average force is. The graph of this function contains important information. The areas under the curves are equal to each other, and are numerically equal to the applied impulse. Notice that the area under each plot has been filled in. Thus, the areas are equal, and both represent the impulse that the meteor applied to Earth during the two-second impact. The average force on Earth sounds like a huge force, and it is.

Nevertheless, Earth barely noticed it. The acceleration Earth obtained was just. That said, the impact created seismic waves that nowadays could be detected by modern monitoring equipment. The collision with the building causes the car to come to a stop in approximately 1 second.

The driver, who weighs N, is protected by a combination of a variable-tension seatbelt and an airbag Figure. In effect, the driver collides with the seatbelt and airbag and not with the building. The airbag and seatbelt slow his velocity, such that he comes to a stop in approximately 2.

The restrained driver experiences a large backward force from the seatbelt and airbag, which causes his velocity to decrease to zero. The forward force from the seatback is much smaller than the backward force, so we neglect it in the solution. Impulse seems the right way to tackle this; we can combine Figure and Figure. The negative sign implies that the force slows him down.

For perspective, this is about 1. Big difference! Significance You see that the value of an airbag is how greatly it reduces the force on the vehicle occupants.

For this reason, they have been required on all passenger vehicles in the United States since , and have been commonplace throughout Europe and Asia since the mids. The change of momentum in a crash is the same, with or without an airbag; the force, however, is vastly different. Recall Figure :. This gives us the following relation, called the impulse-momentum theorem or relation.

The impulse-momentum theorem is depicted graphically in Figure. The first ball strikes perpendicular to the wall. Assume the x -axis to be normal to the wall and to be positive in the initial direction of motion. The momentum direction and the velocity direction are the same. The second ball continues with the same momentum component in the y direction, but reverses its x -component of momentum, as seen by sketching a diagram of the angles involved and keeping in mind the proportionality between velocity and momentum.

Calculate the change in momentum for each ball, which is equal to the impulse imparted to the ball. Let u be the speed of each ball before and after collision with the wall, and m the mass of each ball. Choose the x -axis and y -axis as previously described, and consider the change in momentum of the first ball which strikes perpendicular to the wall.

Impulse is the change in momentum vector. Therefore the x -component of impulse is equal to —2 mu and the y -component of impulse is equal to zero. It should be noted here that while p x changes sign after the collision, p y does not. The direction of impulse and force is the same as in the case of a ; it is normal to the wall and along the negative x- direction.

Forces are usually not constant. Forces vary considerably even during the brief time intervals considered. It is, however, possible to find an average effective force F eff that produces the same result as the corresponding time-varying force. Figure 1 shows a graph of what an actual force looks like as a function of time for a ball bouncing off the floor.

The area under the curve has units of momentum and is equal to the impulse or change in momentum between times t 1 and t 2. That area is equal to the area inside the rectangle bounded by F eff , t 1 , and t 2.

Thus the impulses and their effects are the same for both the actual and effective forces. Figure 1. A graph of force versus time with time along the x-axis and force along the y-axis for an actual force and an equivalent effective force. The areas under the two curves are equal. Then, try catching a ball while keeping your hands still. Hit water in a tub with your full palm.

After the water has settled, hit the water again by diving your hand with your fingers first into the water. Your full palm represents a swimmer doing a belly flop and your diving hand represents a swimmer doing a dive. Explain what happens in each case and why. Which orientations would you advise people to avoid and why? The assumption of a constant force in the definition of impulse is analogous to the assumption of a constant acceleration in kinematics.

In both cases, nature is adequately described without the use of calculus. Skip to main content. Linear Momentum and Collisions. Search for:.