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 illustrations 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 pass 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 glass 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 passenger 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 bump? 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 passing? Why? 15. Why does a bullet when fired through a window make a clean round hole in the glass, while a small stone thrown against the window shatters the glass? 16. A tallow candle can be fired through a pine board. Why? 17. In cyclones, straws are frequently found driven a little distance into trees; why are the straws not broken and crushed instead of being driven into the tree unbroken? 18. A bullet weighing one-half oz. is fired from a gun weighing 8 lb. The bullet has a velocity of 1800 ft. per second. Find the velocity of the "kick" or recoil of the gun.