8. (Pg. 55) Why would they not balance with unequal weights?

9. (Pg. 55) Were the fulcrum removed from the middle of the beam what would result?

10. (Pg. 55) What do we mean by the arms of a lever?

11. (Pg. 56) How may a pair of scales be false, and yet appear to be true?

12. (Pg. 56) If the fulcrum be removed from the centre of gravity, how may the equilibrium be restored?

13. (Pg. 56) How is this exemplified by fig. 3. plate 4?

14. (Pg. 56) What proportion must the weights bear to the lengths of the arms?

15. (Pg. 57) On what principle do we weigh with a pair of steelyards, and what will be the difference in the motion of the extremities of such a lever?

16. (Pg. 58) How is this exemplified by fig. 4. plate 4?

17. (Pg. 58) What line is described by the ends of a lever? fig. 4.

plate 4.

18. (Pg. 58) How many kinds are there; and in the first how is the fulcrum situated?

19. (Pg. 58) When may the fulcrum be so situated that this lever is not a mechanical power, and why?

20. (Pg. 59) What is represented by fig. 5. plate 4?

21. (Pg. 59) Give a familiar example of the use of a lever of the first kind.

22. (Pg. 59) In what instruments are two such levers combined?

23. (Pg. 59) How may two horses of unequal strength, be advantageously coupled in a carriage?

24. (Pg. 60) Describe a lever of the second kind. (Fig. 6. plate 4.)

25. (Pg. 60) What is represented in fig. 7. plate 4, and in what proportion does this lever gain power?

26. (Pg. 60) What is said respecting a door?

27. (Pg. 60) Describe a lever of the third kind.

28. (Pg. 60) In what instance do we use this?

29. (Pg. 61) What remarks are made on its employment in the limbs of animals?

30. (Pg. 61) What are the conditions of equilibrium in every lever?

CONVERSATION V.

CONTINUED.

ON THE MECHANICAL POWERS.

OF THE PULLEY. OF THE WHEEL AND AXLE. OF THE INCLINED PLANE. OF THE WEDGE. OF THE SCREW.

MRS. B.

The pulley is the second mechanical power we are to examine. You both, I suppose, have seen a pulley?

_Caroline._ Yes, frequently: it is a circular, and flat piece of wood or metal, with a string which runs in a groove round it: by means of which, a weight may be pulled up; thus pulleys are used for drawing up curtains.

_Mrs. B._ Yes; but in that instance the pulleys are fixed; that is, they retain their places, and merely turn round on their axis; these do not increase the power to raise the weights, as you will perceive by this figure. (plate 5. fig. 1.) Observe that the fixed pulley is on the same principle as the lever of a pair of scales, in which the fulcrum F being in the centre of gravity, the power P and the weight W, are equally distant from it, and no advantage is gained.

_Emily._ Certainly; if P represents the power employed to raise the weight W, the power must be greater than the weight in order to move it.

But of what use then is a fixed pulley in mechanics?

_Mrs. B._ Although it does not increase the power, it is frequently useful for altering its direction. A single fixed pulley enables us to draw a curtain up, by pulling the string connected with it downwards; and we should be at a loss to accomplish this simple operation without its a.s.sistance.

_Caroline._ There would certainly be some difficulty in ascending to the head of the curtain, in order to draw it up. Indeed I now recollect having seen workmen raise weights to a considerable height by means of a fixed pulley, which saved them the trouble of going up themselves.

_Mrs. B._ The next figure represents a pulley which is not fixed; (fig.

2.) and thus situated, you will perceive that it affords us mechanical a.s.sistance.

A is a moveable pulley; that is, one which is attached to the weight to be raised, and which consequently moves up or down with it. There is also a fixed pulley D, which is only of use to change the direction of the power P. Now it is evident that the velocity of the power, will be double that of the weight W; for if the rope be pulled at P, until the pulley A ascends with the weight to the fixed pulley D, then both parts of the rope, C and B, must pa.s.s over the fixed pulley, and consequently the hand at P, will have descended through a s.p.a.ce equal to those two parts; but the weight will have ascended only one half of that distance.

_Caroline._ That I understand: if P drew the string but one inch, the weight would be raised only half an inch, because it would shorten the strings B and C half an inch each, and consequently the pulley with the weight attached to it, can be raised only half an inch.

_Emily._ But I do not yet understand the advantage of moveable pulleys; they seem to me to increase rather than diminish the difficulty of raising weights, since you must draw the string double the length that you raise the weight; whilst with a single pulley, or without any pulley, the weight is raised as much as the string is shortened.

_Mrs. B._ The advantage of a moveable pulley consists in dividing the difficulty; we must, it is true, draw twice the length of the string, but then only half the strength is required that would be necessary to raise the weight without the a.s.sistance of a moveable pulley.

_Emily._ So that the difficulty is overcome in the same manner as it would be, by dividing the weight into two equal parts, and raising them successively.

_Mrs. B._ Exactly. You must observe, that with a moveable pulley the velocity of the power, is double that of the weight; since the power P (fig. 2.) moves two inches whilst the weight W moves one inch; therefore the power need not be more than half the weight, to make their momentums equal.

_Caroline._ Pulleys act then on the same principle as the lever; the deficiency of weight in the power, being compensated by its superior velocity, so as to make their momentums equal.

_Mrs. B._ You will find, that all gain of power in mechanics is founded on the same principle.

_Emily._ But may it not be objected to pulleys, that a longer time is required to raise a weight by their aid, than without it? for what you gain in power, you lose in time.

_Mrs. B._ That, my dear, is the fundamental law in mechanics: it is the case with the lever, as well as the pulley; and you will find it to be so with all the other mechanical powers.

_Caroline._ I do not see any advantage in the mechanical powers then, if what we gain by them in one way, is lost in another.