The Fly-press.-This machine is used, in the form shown by the figure, either for embossing or stamping pieces of metal with

some design, or for punching thin metal plates. The piece of metal M, to be embossed or punched, is laid on a disc D, and the die or punch P is caused to come down on M with a large amount of stored-up energy, due to the operator taking hold

one or other of the heavy balls B, and giving them a very rapid turn round. The result of this movement is to send the quickly pitched square-double-threaded screw rapidly through its nut N, thereby forcing the guided square carrying the punch straight downwards, and causing the latter to overcome the resistance of the hard metal. Neglecting friction at the screw and the guide, and considering the combined weight of the two balls as= W lbs., and v= their velocity in feet per second at the instant the punch meets the metal M, then

Wv2

ft.-lbs.

2g

If Length the punch or die goes into the metal in feet, And R = Resistance overcome (mean) in lbs.,

Then

Wv3

Rl=

ft.-lbs.

29

LECTURE XXI.—QUESTIONS.

223

LECTURE XXI.—QUESTIONS.

1. A body moves in a circle with a uniform velocity; show that it must be acted on by a constant force tending towards the centre, and find the magnitude of the force in terms of the radius of the circle, and of the mass and velocity of the body.

2. A body weighing 21⁄2 lbs., fastened to one end of a thread 4 feet long, is swung round in a circle, of which the thread is the radius; what will be its velocity when the tension of the thread is a force of 20 lbs. (g=32) ? Ans. 32 feet per second.

3. When an unbalanced wheel is set in rapid rotation, a considerable amount of shake and vibration is experienced. You are required to explain this result from first principles, and to state the mechanical laws which appear to be at work. How would you calculate the amount of pull that this unbalanced weight exerts ?

4. What primary law in mechanics asserts itself when some revolving piece of machinery moves at a high velocity, and is unbalanced? A weight of 1 lb. is placed on the rim of a wheel 2 feet in diameter, which revolves upon its axis and is otherwise balanced. The linear velocity of the rim being 30 feet per second, what is the pull on the axis as caused by the weight of 1 lb.? Ans. 28.1 lbs.

I

5. A segment of a fly-wheel, with the arm to which it is attached, weighs 3500 lbs., and the mass of the portion may be taken as collected at a distance of 8 feet from the axis of the wheel, which makes 40 revolutions per minute. What is the force tending to pull away the segment and arm from the boss of the wheel? (S. and A. Êxam. 1889.) Ans. 15,365 lbs.

6. Define kinetic energy. How does it differ from potential energy? If a velocity of 300 feet per second is impressed on a weight of 10 lbs., what is the measure of the energy now imparted to the weight? (S. and A. Exam. 1891.) Ans. 14,062.5 ft.-lbs.

7. State the rule for finding the amount of work stored up in a given weight when moving with a given velocity. A weight of 6 cwt. moves with a velocity of 20 feet per second; how many units of work are stored up in it? Ans. 4200 ft.-lbs.

8. Write down the formula for the amount of energy stored up in a given weight when moving with a given velocity. Describe, with a sketch, the action of a fly-press. If each ball of the press weighs 50 lbs., and the work stored up in the balls is 400 ft.-lbs., find the velocity with which they are moving. Take the number 32 to represent g. (S. and A. Exam. 1888.) Ans. 16 feet per second.

9. Account for the storing up of energy in a rotating fly-wheel. If the weight of the rim be doubled while the rate of rotation remains unchanged, how much is the energy increased? Ans. Twice.

10. State the formula for the energy stored up in a fly-wheel, on the supposition that the whole of the material is collected in a heavy rim of given mean radius. Apply the formula to show (1) the effect of doubling the number of revolutions per minute; (2) the effect of doubling the weight; (3) the effect of increasing the mean radius in the proportion of 3 to 2. (S. and A. Exam. 1890.)

11. A fly-wheel weighs 2 tons, and its mean rim has a velocity of 40 feet per second. If the wheel gives out 10,000 ft.-lbs. of energy, how much is its velocity diminished? (S. and A. Exam. 1888.) Ans. 1455 feet 1 second.

12. The rim of a fly-wheel weighs 9 tons, and the mean linear velocity of its mass is assumed to be 40 feet per second; how many foot-tons of work are stored up in it? If it be required to store the additional work of 9 foot-tons, what should be the increase of velocity? Ans. 225 ft.-tons; 079 ft. per second.

13. Sketch a fly-press, explain its action, and state for what purpose it is chiefly used. Find, in foot-pounds, the amount of work accumulated in a body which weighs 80 lbs., and has a velocity of 20 feet per second. Ans. 500 ft.-lbs.

14. In a fly-press there are two weights, each of 60 lbs., placed at the ends of an arm which drives the screw; and the velocity of each weight at the instant of striking the blow is 10 feet per second. The die at the end of the screw moves through inch in coming to rest; what mean statical pressure does it exert on the metal subjected to the operation of stamping? Ans. 22,500 lbs.

( 225 )

LECTURE XXII.

CONTENTS.-Some Properties of Materials employed by Mechanics-Essential Properties-Extension-Impenetrability-Contingent Properties - Divisibility — Porosity - Density-Cohesion-Compressibility and Dilatability-Rigidity - Tenacity Malleability - Ductility Elasticity-Fusibility-Load, Stress, and Strain-Total Stress and Intensity of Stress-Tensile Stress and Strain-Example I.-Compressive Stress and Strain Example II.-Limiting Stress or Ultimate Strength -Safe Loads and Elasticity-Limit of Elasticity-Hooke's LawFactors of Safety-Modulus of Elasticity-Ratio of Stress to StrainExample III.-Questions.

Some Properties of Materials employed by Mechanics. -The properties of matter are almost innumerable, but they may be divided into two classes: (1) Essential properties; (2) Contingent properties. The essential properties are those without which matter cannot possibly exist. The contingent properties are those which we find matter possessing, but without which we could conceive it to exist.

Essential Properties-1. Extension means that property by which every body must occupy a certain bulk or volume. When we say that one body has the same volume as another, we do not mean that it has the same quantity of matter, but only that it occupies the same space.*

2. Impenetrability means that every body occupies space to the exclusion of every other body, or that two bodies cannot exist in the same space at the same time.

Contingent Properties.-1. Divisibility means that matter may be divided into a great but not an infinite number of parts. The ultimate particles of matter are termed atoms, derived from a Greek word signifying indivisible.

2. Porosity signifies that every body contains throughout its mass atomic spaces or interstices to a greater or less extent. These spaces are filled with ether or gas. This has been proved

to be the case with every known substance.

For example, when the steel or cast-iron cylinder of a hydraulic

* For Simple Rules of Mensuration see the Author's Elementary Manual on "Steam and the Steam Engine," Lectures I. II. III.

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