5. Kinds of Force

You hold a book in your hand. If you open your hand, the book will drop to the floor immediately. The cause is the force of gravity that works on the book. When a hammer strikes the head of a nail, the nail is driven into a piece of wood. (See Figure 35.) A sled will stop when it reaches an area that is not covered with snow or ice. (See Figure 36.) Since these phenomena stem from forces that work on them, we know that there are many kinds of force around us. How are they made use of in judo? Let us now study them from this standpoint.

Muscular force

According to Newton's second law of motion, you have an advantage over your opponent when your body is larger than his. Besides that law, however, there is another factor that gives you advantage over a smaller opponent. This is the large muscular force with which a big man is usually gifted. He can carry a heavy block or lift it easily with both hands, whereas the same feat may be difficult for a smaller man.

Although we can say that large muscular force is very convenient for breaking the opponent's posture in judo, muscular force alone does not encompass all the forces used in judo. To make use of muscu­lar force normally and effectively, you must study its nature.

A human body is built up of about 200 bones covered and connected by 500 muscles. As Figure 37 shows, each end of a muscle is attached to a bone, with one or more joints between both ends. A muscle pulls together the two bones to which its ends are attached. Let us explain how the joints are made to bend. Look at Figure 37.

One end of the biceps is attached to the upper part of the ulna. One end of the triceps is attached to the upper part of the radius. When the biceps begins to contract, the forearm begins to rotate about the elbow with the pull of the contracting biceps. If the triceps begins to contract, the forearm begins to rotate inversely about the joint. Thus the arm is straightened. It is obvious that the larger the power of the contracting biceps, the larger the weight the forearm can lift.

Let us call this power of contraction muscular force. The larger the muscle, the larger the muscular force. The force of two arms is, of course, stronger than that of one arm. A block of a certain weight that we cannot lift with one arm may be lifted easily if both arms are used. The work can be done even more easily if we do the lifting with all our muscular force by assuming the posture shown in Figure 38: with both legs bent and the center of gravity lowered.

If the body posture is not correct, and the back is not erect, and the center of gravity in the abdominal region is not stable, then the arms alone will be called upon to do the majority of work in lifting the bar bell. On the contrary, if the back is held erect and the center of gravity in the abdominal area is supported by a balanced stance, with the feet spread to about the width of the shoulders, the large muscles of the abdominal region and the legs are brought into play to support the muscles of the upper region. One of the important facts about judo is that successful employment of techniques is the result of total body muscular movement—as, for example, in the execution of an over-shoulder throw.

37. Muscular contraction.
G : point of exertion             C : triceps
0 : fulcrum D: biceps
0': point of application         E : ulna
P : pull       P : radius

38. Partial   and  total   muscular force.

The same thing can be said about making one's opponent fall or about strangling him. Defensively, too, it might be difficult to save yourself from your opponent's attack were it not for your ability to use all your muscular force. In bending your opponent's joints in reverse, the same rule applies. We can therefore understand that the exertion of a strong force means that muscles must act together by the use of the force of the waist and abdominal region.

We know that coordinated muscular force can give our bodies quick or slow, weak or strong motions at our will. This is what enables you to pull up a heavy block from the ground by making use of the force of reaction that will be produced when you kick the ground with your legs, or when you push a weight high above your head, as explained in Chapter 4. In judo you can pull your opponent's body against yours with your arms as in hane-goshi (spring hip throw—Figure 80) or harai-goshi (sweeping loin—Figure 79). In o-uchi-gari (major internal reaping—Figure 86) or ko-uchi-gari (minor internal reaping —Figure 87), you push your opponent backward to the mat with your hand. You must remember, however, that the force that pulls or pushes horizontally is not a muscular force (force of arm) as described in the passage on the third law of motion.

Let us consider the functions of the arm. If your hands pull your opponent horizontally, they serve as chains that tightly tie his body to yours. If you push him back, your arms serve as poles that can not be bent. Besides this, there is another important work accom­plished by the force of the arms. This function will be explained below in the section on momentum, which will clarify the limits of the force of the arm.

Expert judo is characterized by a large variety of techniques. As you observe, you will notice that the expert makes good use of many kinds of forces. Since judo employs many forces, such as those of gravity, momentum, and friction, you must not mistake muscular force for the only effective one. If you do, your judo will become hard, heavy, slow, and ineffective.

Gravity

In judo it is important to throw your opponent by making use of his loss of balance, as we noted in Chapter 3. One of the laws at work here is the law of gravity. We know that Sir Isaac Newton discovered the law of gravitation by seeing an apple fall from a tree. All bodies in the universe attract one another. For instance, the earth attracts the bodies near and around it. In turn they also pull the earth. Since the power of attraction, according to Newton, is propor­tional to the mass of the body that attracts, the larger the mass of the body, the larger its attraction. All bodies near the earth fall to the earth because it has an immense mass. An airplane or a bird starts to fall to the ground as soon as its power of flight is exhausted. The force of attraction between the earth and a two-pound weight is twice that between the earth and a one-pound weight. The attraction be­tween the earth and a body is called gravity. When gravity is repre­sented by weight units, it is called weight.

Now let us consider the application of the law of gravity to judo. The heavier the opponent, the more difficult it is for you to move him horizontally. It is even more difficult for you to move him vertically. On the other hand, a larger gravity acts on him to make him fall. In judo gravity may be represented as a force pulling the opponent down­ward. If you want to make him fall, you make him lose his balance; that is, you cause his center of gravity to go outside the base. Then the gravity that acts on him works for you to make him lean or fall. Let us study the action of the law of gravity by illustrations.

40. Center of gravity at fulcrum;  equal weight on both sides.

Look at Figure 39. You (A) and your opponent (B) are standing face to face. He advances toward you to take hold of you by the left lapel. At the same time you withdraw as much as he advances. If he is mentally or physically unable to let his advanced foot advance again, he will lean forward, lose his balance, and fall. Also, it is obvious that the same thing will happen when the stability of the legs supporting the trunk is taken away. When your opponent takes a larger step forward than usual, you merely sweep his advanced foot away in the direction of his advance, as illustrated in Figure 83 (de-ashi-harai, or advanced foot sweep). By doing this, you will drop him with the gravity acting on him directly.

Finally let us consider a case in which the opponent is downed by the nullification of his resistance to gravity. It may be difficult for you, because of the weight advantage of your opponent, to lift him with your arms. But it is easy to support him at the center of gravity with your loins as he leans forward. Look at the seesaw in Figure 40. A long board is supported at the center of gravity, so that the gravity on one side is equal to that on the other. Thus a slight force can rotate the board around the fulcrum. After making your opponent lean for­ward, support him at the center of gravity with your loins. No matter how much weight he may have, a slight pull can rotate him around your loins. To support your opponent completely at the center of gravity with your loins is the key point of such hip throws as o-goshi, o-tsuri-goshi, ko-tsuri-goshi, hane-goshi, etc. For further theoretical points of these techniques, see the discussion of moment of force in Chapter 6.

Momentum

Why is it that a little man who is proficient in judo cannot be moved even by a large man with less experience? In grappling, the smaller man handles his opponent with the ease of a mother who cuddles her baby on her lap. Where does this wonderful force come from?

41. Momentum  plus  muscular  force  beats muscular force alone.

42. Momentum supplements muscular force in a throw. Contact of sweeping foot transfers force to op­ponent's ankle in okuri-ashi-harai.

It comes from the momentum produced by a body in motion. Even now some of the secrets of the force of momentum seem hidden by a veil of ignorance. The secret is in the force of the waist and ab­dominal region: a force that only a great master can have at his complete control. The function of this force we have already studied in Chapter 3. Let us now look into the nature of momentum.

A blacksmith always uses a hammer when he strikes an iron bar. All of us know that the larger the striking velocity, the larger the effect upon the nail or iron bar that is struck by a hammer. Through this illustration you will see that a new force is produced in a body when it moves. This force equals the product of the weight (m) of a body and its speed (v) of motion. The product mv is called momentum. Its value is so large that everyone is surprised at seeing the product. For instance, if a body of one kilogram moves at a velocity of ten meters per second, the momentum is figured as follows: Momentum=mv (weightxvelocity)

=l kgxl0m

=l kgx1,000 cm

=1,000 kgcm per second This figure means that the momentum equals that of a body of 1,000 kilograms moving at a velocity of one centimeter per second. There­fore, to stop in a unit time a one-kilogram body moving at a velocity of ten meters per second, a 1,000-kilogram resistance body will be needed. And thus a little man can win over a stronger man because of his speed.

Review the above-cited figures again. It should be clear that you, even though you may not be very large in stature, can easily throw your opponent if your attack is fast enough. Figure 42 illustrates an instance in which momentum is used to supplement muscular force. How to produce as much momentum as possible and induce it effec­tively in your opponent in grappling will be explained in Chapter 8. For the present let us study the law under which momentum will be induced in your opponent when you strike against him. We shall discuss this subject under four divisions: impulse, impulsive force, the application of the strongest possible force on the opponent, and the relation of momentum to the force of the arm.

43.  Impulse and impulsive force.

1.    Impulse

Drop an iron ball and try to stop it on its way down. First, stop it slowly with your hand, then stop it quickly in the shortest time possible. You will find that in the first case a comparatively small force is needed, but in the latter case a larger force is required. This is because of the law which asserts that the stopping force is propor­tional to the product of the mass and velocity of the body in motion and is in inverse proportion to the time required to stop that body. For instance, take the weight of the hammer, the velocity of its motion when it touches the iron bar, and the time and force required to stop it as m, v, t, and f, respectively. We then have the following equation:

ft=mv (force x time=weightxvelocity)

We can now easily understand why we could stop a ball with a small force the first time but needed a larger force the second time. Suppose that mv (weight x velocity) is constant. Then the larger the time t, the smaller the force /. The product of the time and the force required to stop an advancing body is called impulse.

2.         Impulsive force

Assume that the time required to stop a striking body is near zero. Then, from the above equation, we see that the force required to stop it will become nearly equal to the momentum. In such a case, when an attacking body is stopped in an extremely short time, the product of the force and the time is called impulsive force. We can see many examples of impulsive force every day: the striking of a ball with a bat, the blows at a boxing match, and the kicking of a foot against the ground when we jump.

3.         How  to  apply  the  strongest  force   possible   on   the opponent

In judo, in order to apply a large force to your opponent, you must induce momentum in him in the shortest time possible as well as make the m (weight) express your whole weight and enlarge the v (velocity) so that mv will become greater. Let us cite an example of what makes the time t smaller in judo.

Look at harai-goshi in Figures 44 and 45. If you (A) sweep up the right leg of your opponent with your right leg while suddenly pulling his upper body with your hands in the direction shown by the arrow, he will be thrown down, rotating forward. In this case you turn to the left as quickly as possible by taking the posture shown in Figures 44 and 45. The momentum will be produced in your body.

44. Harai-goshi: less effective means of inducing momentum is to grip opponent's left lapel and right sleeve.

45. Harai-goshi: more effective means of inducing momentum is to place your right hand under opponent's armpit and hold his right arm be­tween your left arm and chest.

There are two ways for you to induce momentum in your opponent's upper body with your hands. (See Figure 44.) One is by gripping him by his left front lapel with your right hand and by the sleeve with your left hand. The other method (see Figure 45) is that of putting your right hand under his left armpit, at the same time holding his right arm between your left arm and the left part of your chest.

In both cases the same momentum mv will be induced in him by your hands. But the time required to stop your body will be different. Consider which is the better of the two ways. Of course it is the latter, since in the former your opponent's lapel and sleeve serve as springs to make the time t longer.

In conclusion let us consider a few cases that make use of the large t. When we jump to the ground from a high place, we land on our toes first and then on our heels. We never land on our heels first. Why? Suppose your weight is 75 kilograms. Then there will be produced a large momentum until your feet touch the ground, and your feet may be injured by the impulsive force produced when they strike against the ground. But when you touch down tiptoe first, the joints of both ankles serve as springs to prevent an impulsive force. If you are thrown on the mat by your opponent, the impulsive force will injure your body unless preventive measures are taken. For this reason we are taught ukemi (ways of falling)—that is, how to make use of the joints of the shoulders, arms, and legs as springs—to prevent the creation of a force when the body strikes against the mat. We also use floors supported by springs and covered with mats for that purpose in our do jo, or places of judo practice.

Friction

If you push a heavy block on ice, it will slide freely. If a floor is oiled, we may slip and fall on it even if we walk carefully. But if the floor is rough, there is little danger of slipping. In judo we are sometimes easily made to slip on the mat. For solution of this problem we shall now study the law of friction.

Our daily experience shows us that when a block is being acted upon by a force, it will slide along a plane, but that a force that tries to prevent the block from moving is produced between the two surfaces of contact. The resisting force is usually called friction. Let us study the nature of friction. We can observe that it involves three principles.

1. The friction between two surfaces is proportional to the force pressing them together. In the apparatus shown in Figure 46 the block A has six plane surfaces, and the weight W weighs w kilograms. Suppose that W has just enough power to pull A in the direction of the pulley. Friction will be produced between the two surfaces in contact when the weight is allowed to pull the block. Let us call the friction F. Now let us place another block, B, of the same weight as A, on top of A while putting a weight W, of the same weight as W, on top of W. In this case, too, the two weights can pull the piled
   blocks. Thus we can see that the friction F then produced is twice the friction F formerly produced. If a third block and a third weight are added, the friction is three times as much as the first friction F. We also know that the heavier the man, the more difficult it is to make him slide or slip.
2. The friction between two surfaces depends upon the nature of their surfaces of contact. If oil is applied to the two surface of contact, we know that the friction between them becomes very small. The reason we slip easily and fall when we walk on a frosted road is that the friction between the road and our shoes is very small. In judo we are very familiar with the fact that if the mat is slippery, such footsweeping techniques as de-ashi-harai and okuriashi-harai are especially effective.
3. The friction between two surfaces is independent of the area of the surfaces of contact. An experiment will show that the friction F' produced if the block A is turned on its side will be the same as the friction F produced in the first experiment. We can therefore understand that there is no change of friction whether one stands on one foot, on both feet, or on tiptoe.

Coefficient of friction

Since the friction (tangential force) changes proportionally to the force pressing two surfaces together (normal force), the ratio when he steps forward, together with the force with which you sweep his foot, will work to overcome the friction. (Read Chapter 7, section on de-ashi-harai.)

Next let us study how you can defend yourself from hane-goshi (spring hip throw) by taking advantage of friction. Look at Figure 47. Your posture is not broken yet, but your opponent tries to apply hane-goshi. Friction created between the mat and the sole of your foot keeps you from rotating; your weight presses down the surfaces in contact. What prevents you from falling forward in this case is friction. Therefore, if you keep a natural posture, it is difficult for you to be thrown.

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