Using Impulse to Increase Momentum
The task in many sport skills is to cause a large change in the velocity of something. In throwing events, the ball (or shot, discus, javelin, or Frisbee) has no velocity at the beginning of the throw, and the task is to give it a fast velocity by the end of the throw. We want to increase its momentum. Similarly, in striking events, the racket (or bat, fist, club, or stick) has no velocity at the beginning of the swing (or stroke or punch), and the task is to give the implement a fast velocity just before its impact. Our bodies may be the objects whose momentum we want to increase in jumping events and other activities. In all of these activities, the techniques used may be explained in part by the impulse–momentum relationship. A large change in velocity is produced by a large average net force acting over a long time interval. Because there are limits on the forces humans are capable of producing, many sport techniques involve increasing the duration of force application. Try self-experiment 3.6 to see how force duration affects performance.
Take a ball in your throwing hand and see how far (or how fast) you can throw it using only wrist motions. Move only your hand and keep your forearm, upper arm, and the rest of your body still. This is not a very effective technique, is it? Now try to throw the ball again, only this time use your elbow and wrist. Move only your hand and forearm, and keep your upper arm and the rest of your body still. This technique is better, but it still isn’t very effective. Try it a third time using your wrist, elbow, and shoulder. Move only your hand, forearm, and upper arm, and keep the rest of your body still. This technique is an improvement over the previous one, but you could still do better. Try it a fourth time throwing as you normally would with no constraints. This throw was probably the fastest. In which throw were you able to exert a force against the ball for the longest amount of time? For the shortest amount of time?
During self-experiment 3.6, you exerted the largest impulse on the ball when you used your normal throwing technique. As a result, the ball’s momentum changed very much, and the ball left your hand with the fastest velocity. The large impulse was the result of a relatively large average force being exerted on the ball for a relatively long time. You exerted the smallest impulse on the ball when you used only your wrist. The ball’s momentum didn’t change very much, and the ball left your hand with the slowest velocity. The small impulse was the result of a relatively small average force being exerted on the ball for a relatively short time. The normal throwing technique involved more limbs in the throwing action, and you were able to increase the time during which you could exert a force on the ball (and you were probably able to exert a larger average force). The end result was a faster throw. Due to a longer period of force application, the ball had more time to speed up, and thus its velocity at release was faster.
An important thing to remember about the impulse–momentum relationship (equation 3.29),
ΣF–Δt = m(vf − vi),
is that the average net force, ΣF–, in the impulse term is a vector, as are the velocities, vf and vi, in the momentum term. An impulse will cause a change in momentum, and thus a change in velocity, in the direction of the force. If you want to change the velocity of an object in a specific direction, the force you apply, or some component of that force, must be in that specific direction.
Which is the greater limitation on impulse—the force or the time? Try self-experiment 3.7 to help answer this question.
See how far (or fast) you can throw a very light object (such as a table tennis ball) compared to a very heavy object (such as a 16 lb [7.3 kg] shot). What limited your throwing performance with the lighter object? Was your strength the limiting factor (do you have to be exceptionally strong to throw a table tennis ball fast?) or was it technique (duration of force application)? What limited your throwing performance with the heavy object—strength (force) or technique (duration of force application)?
In self-experiment 3.7, the limiting factor for throwing the very light object was your technique, not your strength. More specifically, the duration of time during which you could exert a force on the ball was constrained. It was very short. The ball sped up so quickly that your hand had a difficult time keeping up with it and still exerting a force on it.
Conversely in this experiment, the limiting factor for throwing the very heavy object was your strength, not your technique. When you tried to throw (or put) the 16 lb shot, the limiting factor was not the duration of the force application but the size of the force itself. The force you exerted was definitely larger than the force exerted when you threw the table tennis ball, but the amount of force you exerted was constrained by your strength. If you were stronger, the force you could exert on the shot would have been larger, and the shot would have gone farther and faster.
When you threw the table tennis ball in self-experiment 3.7, the average net force, ΣF–, wasn’t the problem; the time of its application, Δt, was. In the shot put, the time of application was long, but the amount of force applied was limited. In both instances, maximizing both quantities, ΣF–and Δt, will result in the fastest throw or put. But in throwing a lighter object, technique (duration of force application) is more important for success, whereas in throwing heavy objects, the force applied is more important. Compare baseball pitchers and javelin throwers to shot-putters. Shot-putters are bigger and stronger. Their training and selection have been based on their ability to produce large forces (ΣF– in impulse). Baseball pitchers and javelin throwers are not as strong. They’re successful because their techniques maximize the duration of force application (Δt in impulse).
Now let’s try an activity in which the force element of the impulse is constrained so that we are forced to emphasize duration of force application (Δt) in the impulse equation. Try self-experiment 3.8.
Fill several balloons with water so that each one is about the size of a softball. Take these balloons outside to an empty field or empty parking lot. Now, see how far you can throw one without having it break in your hand. If you exert too large a force against the balloon, it will break. To throw the balloon far, you must maximize the duration of force application during the throw while limiting the size of the force you exert against the balloon so that it doesn’t break. Don’t constrain your technique to what you perceive as normal throwing styles. Remember, the best technique will be the one in which you accelerate the balloon for the longest possible time while applying the largest (but non-balloon-breaking) force against the balloon.
Let’s summarize what we’ve learned about impulse and momentum so far. The relationship is described mathematically by equation 3.29:
impulse = change in momentum
ΣF– = average net force acting on an object,
Δt = interval of time during which this force acts,
m = mass of the object being accelerated,
vf = final velocity of the object at the end of the time interval, and
vi = initial velocity of the object at the beginning of the time interval.
In many sport situations, the goal is to impart a fast velocity to an object. The initial velocity of the object is zero, and the final velocity is fast, so we want to increase its momentum. We accomplish this by exerting a large force against the object for as long a time as possible (by exerting a large impulse). Techniques in sport activities such as throwing or jumping are largely based on increasing the time of force application to obtain a large impulse.