=76. Momentum.=--It is a matter of common observation that a heavy body is set in motion with more difficulty than a light one, or if the same force is used for the same length of time upon a light and a heavy body,[E] the light body will be given a greater velocity. This observation has led to the _calculation_ of what is called the "quant.i.ty of motion" of a body, or its _momentum_. It is computed by multiplying the ma.s.s by the velocity. If the C.G.S. system is used we shall have as the momentum of a 12 g. body moving 25 cm. a second a momentum of 12 25 or 300 C.G.S. units of momentum. This unit has no name and is therefore expressed as indicated above. The formula for computing momentum is: _M = mv_.

[E] By a light body is meant one of small ma.s.s, a heavy body possessing much greater ma.s.s.

Newton's Laws of Motion

=77. Inertia, First Law of Motion.=--One often observes when riding in a train that if the train moves forward suddenly the pa.s.sengers do not get into motion as soon as the train, and apparently are jerked backward.

While if the train is stopped suddenly, the pa.s.sengers tend to keep in motion. This tendency of matter to keep moving when in motion and to remain at rest when at rest is often referred to as the property of _inertia_. _Newton's first law of motion_, often called the _law of inertia_, describes this property of matter as follows:

_Every body continues in a state of rest or of uniform motion in a straight line unless it is compelled to change that state by some external force._ This means that if an object like a book is lying on a table it will remain there until removed by some outside force. No inanimate object can move itself or stop itself. If a ball is thrown into the air it would move on forever if it were not for the _force_ of attraction of the earth and the resistance of the air.

It takes time to put a ma.s.s into motion, a heavy object requiring more time for a change than a light object. As an example of this, note the movements of pa.s.sengers in a street car when it starts or stops suddenly. Another ill.u.s.tration of the law of inertia is the so-called "penny and card" experiment. Balance a card on the end of a finger.

Place on it a coin directly over the finger, snap the card quickly so as to drive the card from beneath the coin. The coin will remain on the finger. (See Fig. 59.)

[Ill.u.s.tration: FIG. 59.--The ball remains when the card is driven away.]

According to Newton's first law of motion a moving body which could be entirely freed from the action of all external forces would have uniform motion, and would describe a perfectly straight course. The curved path taken by a baseball when thrown shows that it is acted upon by an outside force. This force, the attraction of the earth, is called _gravity_.

[Ill.u.s.tration: SIR ISAAC NEWTON "By Permission of the Berlin Photographic Co., New York."

Sir Isaac Newton (1642-1727) Professor of mathematics at Cambridge university; discovered gravitation; invented calculus; announced the laws of motion; wrote the Principia; made many discoveries in light.]

[Ill.u.s.tration: GALILEO GALILEI "By Permission of the Berlin Photographic Co., New York."

Galileo Galilei (1564-1642). Italian. "Founder of experimental science"; "Originator of modern physics"; made the first thermometer; discovered the laws of falling bodies and the laws of the pendulum; invented Galilean telescope.]

[Ill.u.s.tration: FIG. 60.--Cross-section of the DeLaval cream separator.]

=78. Curvilinear Motion.=--Curvilinear motion occurs when a moving body is pulled or pushed away from a straight path. The pull or push is called _centripetal_ (center-seeking) force. A moving stone on the end of a string when pulled toward the hand moves in a curve. If the string is released the stone moves in a tangent to the curve. The string pulls the hand. This phase of the pull is called _centrifugal_ force. The _centripetal_ force is the pull on the stone. Centripetal and centrifugal force together cause a tension in the string. Examples of curvilinear motion are very common. The rider and horse in a circus ring lean inward in order to move in a curve. The curve on a running track in a gymnasium is "banked" for the same reason. Mud flying from the wheel of a carriage, the skidding of an automobile when pa.s.sing rapidly around a corner, and sparks flying from an emery wheel, are ill.u.s.trations of the First Law of Motion.

Cream is separated from milk by placing the whole milk in a rapidly revolving bowl, the cream being lighter collects in the center and is thrown off at the top. (See Fig. 60.) Clothes in steam laundries are dried by a centrifugal drier. In amus.e.m.e.nt parks many devices use this principle. (See centrifugal pumps, Art. 70.)

[Ill.u.s.tration: FIG. 61.--The two b.a.l.l.s reach the floor at the same time.]

=79. The Second Law of Motion,= sometimes called the _law of momentum_, leads to the _measurement of force_, by the momentum or the quant.i.ty of motion, produced by it. The law is stated as follows:

_Change of motion, or momentum, is proportional to the acting force and takes place in the direction in which the force acts._ In other words, if two or more forces act at the same instant upon a body each produces the same effect that it would if acting alone. If a card be supported on two nails driven horizontally close together into an upright board (see Fig. 61), and two marbles be so placed on the ends as to balance each other, when one marble is snapped horizontally by a blow, the other will fall. Both reach the floor at the same time. The two b.a.l.l.s are equally pulled down by the earth's attraction and strike the ground at the same time, though one is shot sidewise, and the other is dropped vertically.

As gravity is a constant force, while the blow was only a momentary force, the actual path or resultant motion will be a curved line.

The constant relation, between the acting force and the change of momentum it produces in a body, has led to the adoption of a convenient C.G.S. unit of force called the _dyne_. _The dyne is that force which can impart to a ma.s.s of one gram a change of velocity at the rate of one centimeter per second every second._ This definition a.s.sumes that the body acted upon is free to move without hindrance of any kind, so that the acting force has to overcome only the _inertia_ of the body.

_However_, the _law_ applies in every case of application of force, so that each force produces its full effect independently of other forces that may be acting at the same time upon the body.

=80. Newton's Third Law.=--This law has been experienced by everyone who has jumped from a rowboat near the sh.o.r.e. The muscular action that pushes the body forward from the boat also pushes the boat backward, often with awkward results. The law is stated: _To every action, there is always an opposite and equal reaction, or the mutual actions of any two bodies are always equal and opposite in direction_. Many ill.u.s.trations of this law are in every one's mind: a stretched rope pulls with the same force in one direction as it does in the opposite direction. If a bat hits a ball, the ball hits the bat with an equal and opposite force. The third law is therefore sometimes called the law of _reaction_. When a weight is hung upon a spring balance the action of the weight pulls down the spring until it has stretched sufficiently (Hooke's Law) to produce an elastic _reaction_ that equals and hence supports the weight. When a man stands at the center of a plank supported at its ends, the action of the man's weight bends the plank until the elastic force developed in the plank equals the weight applied. Further, when a train or a wagon is on a bridge the bridge yields until it has developed an elastic reaction equal to the weight applied. If a person stands in the center of a room, the floor beams yield until the third law is satisfied. In fact, whenever a force acts, a contrary equal force always acts.

=81. Stress and Strain.=--A pair of forces that const.i.tute an action and a reaction is called a _stress_. The two forces are two parts of one _stress_. If the two forces act away from each other, as in the breaking of a string, the stress is called a _tension_, but if they act toward each other as in crushing anything, the stress is called a _pressure_.

In order for a body to exert force it must meet with resistance. The force exerted is never greater than the resistance encountered. Thus one can exert but little force upon a feather floating in the air or upon other light objects. A fast moving shot exerts no force unless it encounters some resistance.

Forces, then, are always found in pairs. Thus to break a string, to stretch an elastic band, to squeeze a lemon, one must exert two equal and opposite forces. Such a thing as a single force acting alone is unknown. Usually, however, we give our attention mainly to one of the forces and ignore the other. When a force acts upon a body the change of shape or size resulting is called a _strain_. Hooke's law (Art. 32) is often expressed as follows: "The strain is proportional to the stress,"

_e.g._, the stretch of the spring of a spring balance is proportional to the load placed upon it.

Important Topics

1. Motion a change of position. Kinds of motion.

2. Newton's laws of motion.

3. Momentum.

4. Inertia. First law of motion. Curvilinear motion.

5. Second law of motion.

6. Third law of motion. Action and reaction, stress and strain.

Exercises

1. Mention three ill.u.s.trations of the third law, different from those given.

2. A rifle bullet thrown against a board standing upon edge will knock it down; the same bullet fired at the board will pa.s.s through it without disturbing its position. Explain.

3. A hammer is often driven on to its handle by striking the end of the latter. Explain.

4. Consider a train moving 60 miles an hour, with a gun on the rear platform pointing straight backward. If a ball is fired from the gun with a speed of 60 miles an hour, what will happen to the ball?

5. Could one play ball on the deck of an ocean steamer going 25 miles an hour without making allowance for the motion of the ship? Explain.

6. On a railroad curve, one rail is always higher. Which? Why?

7. Why can a small boy when chased by a big boy often escape by dodging?

8. Will a stone dropped from a moving train fall in a straight line?

Explain.

9. A blast of fine sand driven against a sheet of gla.s.s soon gives it a rough surface. Explain.

10. Explain the use of fly-wheels in steadying the motion of machinery (for example, the sewing machine).

11. Is it easier to walk to the front or rear of a pa.s.senger train when it is stopping? Why?

12. Why does lowering the handles of a wheel-barrow on the instant of striking make it easier to go over a b.u.mp?

13. Why should a strong side wind interfere with a game of tennis? How can it be allowed for?

14. On which side of a railroad track at a curve is it the safer to walk while a train is pa.s.sing? Why?

15. Why does a bullet when fired through a window make a clean round hole in the gla.s.s, while a small stone thrown against the window shatters the gla.s.s?