4. A ball thrown across the ice started with a velocity of 80 ft. per second. It was retarded by friction at the rate of 2 ft. per second each second. How long did it roll? How far did it roll? 5. A bullet was fired with a velocity of 2400 ft. per second from a rifle having a barrel 2 ft. long. Find (a) the average velocity of the bullet while moving the length of the barrel; (b) the time required to move through the barrel; (c) the acceleration of the bullet while in the barrel. 6. A ball was thrown vertically into the air with a velocity of 160 ft. per second. How long did it remain in the air? (Take g=32 ft. per sec2.) 7. A baseball was thrown upward. It remained in the air 6 sec. With what velocity did it leave the hand? How high did it go? 8. A ball dropped from the top of the Woolworth Building in New York City, 780 ft. above Broadway, would require how many seconds to fall? With what velocity would it strike? (Take g = 32 ft. per sec2.) 9. How high was an airplane from which a bomb fell to earth in 10 sec.? 10. With what speed does a bullet strike the earth if it is dropped from the Eiffel Tower, 335 m. high? 11. If the acceleration of a marble rolling down an inclined plane is 20 cm. per second, what velocity will it have at the bottom, the plane being 7 m. long? 12. If a man can jump 3 ft. high on the earth, how high could he jump on the moon, where g is as much? FIG. 84 13. The brakes were set on a train running 60 mi. per hour, and the train stopped in 20 sec. Find the acceleration in feet per second each second and the distance the train ran after the brakes were applied. 14. How far will a body fall from rest during the first half second? 15. With what velocity must a ball be shot upward to rise to the height of the Washington Monument (555 ft.)? How long before it will return? 16. Fig. 84 represents the pendulum and escapement of a clock. The escapement wheel D is urged in the direction of the arrow by the clock weights or spring. The slight pushes communicated by the teeth of the wheel keep the pendulum from dying down. Show how the length of the pendulum controls the rate of the clock. 17. What force supports an airplane in flight? What is "gliding"? 18. A pendulum that makes a single swing per second in New York City is 99.3 cm., or 39.1 in., long. Account for the fact that a seconds pendulum at the equator is 39 in. long, while at the poles it is 39.2 in. long. 19. How long is a pendulum whose period is 3 sec.? 2 sec.? sec.? sec.? 20. A man was let down over a cliff on a rope to a depth of 500 ft. What was his period as a pendulum? NEWTON'S LAWS OF MOTION 99. First law-inertia. It is a matter of everyday observation that bodies in a moving train tend to move toward the forward end when the train stops and toward the rear end when the train starts; that is, bodies in motion seem to want to keep on moving, and bodies at rest to remain at rest. Again, a block will go farther when driven with a given blow along a surface of glare ice than when knocked along an asphalt pavement. The reason which everyone will assign for this is that there is more friction between the block and the asphalt than between the block and the ice. But when would the body stop if there were no friction at all? Astronomical observations furnish the most convincing answer to this question, for we cannot detect any retardation at all in the motions of the planets as they swing around the sun through empty space. Furthermore, since mud flies off tangentially from a rotating carriage wheel, or water from a whirling grindstone, and since, too, we have to lean inward to prevent ourselves from falling outward in going around a curve, it appears that bodies in motion tend to maintain not only the amount but also the direction of their motion (see gyrocompass opposite p. 223). In view of observations of this sort Sir Isaac Newton, in 1686, formulated the following statement and called it the first law of motion. Every body continues in its state of rest or uniform motion in a straight line unless impelled by external force to change that state. This property, which all matter possesses, of resisting any attempt to start it if at rest, to stop it if in motion, or in any way to change either the direction or amount of its motion, is called inertia. 100. Centrifugal force. It is inertia alone which prevents the planets from falling into the sun, which causes a rotating sling to pull hard on the hand until the stone is released, and which then causes the stone to fly off tangentially. It is inertia which makes rotating liquids move out as far as possible from the axis of rotation (Fig. 85), which makes flywheels sometimes burst, which makes the equatorial diameter of the earth greater than the polar, which makes the heavier milk move out farther than the lighter cream in the dairy separator (see opposite p. 85), etc. Inertia manifesting itself in this tendency of the parts of rotating systems to move away from the center of rotation is called centrifugal force. FIG. 85. Illustrating centrifugal force 101. Momentum. The quantity of motion possessed by a moving body is defined as the product of the mass and the velocity of the body. It is commonly called momentum. Thus, a 10-gram bullet moving 50,000 centimeters per second has 500,000 units of momentum; a 1000-kg. pile driver moving 1000 centimeters per second has 1,000,000,000 units of momentum; etc. We shall always express momentum in C.G.S. units, that is, as a product of grams by centimeters per second. 102. Second law. Since a 2-gram mass is pulled toward the earth with twice as much force as is a 1-gram mass, and since both, when allowed to fall, acquire the same velocity in SIR ISAAC NEWTON (1642-1727) English mathematician and physicist, "prince of philosophers' professor of mathematics at Cambridge University; formulated the law of gravitation; discovered the binomial theorem; invented the method of the calculus; announced the three laws of motion which have become the basis of the science of mechanics; made important discoveries in light; is the author of the celebrated "Principia" (Principles of Natural Philosophy), published in 1687 The milk is poured into a central tube (see 1, a) at the top of a nest of disks (see 1 and 4) situated within a steel bowl. The milk passes to the bottom of the central tube, then rises through three series of holes (see 1, b, b, b, etc.) in the nest of disks, and spreads outward into thin sheets between the slightly separated disks. By means of a system of gears (see 3) the disks and bowl are made to revolve from 6000 to 8000 revolutions per minute. The separation of cream from skim-milk is quickly effected in these thin sheets; the heavier skim-milk (water, casein, and sugar) is thrown outward by centrifugal force against the under surfaces of the bowl disks (see 5), then passes downward and outward along these under surfaces to the periphery of the bowl (see 1, d, d, d, etc.), and finally rises to the skim-milk outlet. The lighter cream is thereby at the same time displaced inward and upward along the upper surfaces of the bowl disks (see 5), then passes over the inner edges of the disks to slots (see 1, c, c, c, etc.) on the outside of the central tube, finally rising to the cream outlet, which is above the outlet for the skim-milk (see 1 and 2) |