LECTURE VI.

CONTENTS.-Pulleys-Snatcn Block-Block and Tackle -Theoretical Advantage-Velocity Ratio-The Principle of Work applied to the Block and Tackle-Actual or Working_Advantage-Work put in-Work got out-Efficiency-Percentage Efficiency-Example I.-Questions. Pulleys. Suppose you had to elevate a sack of flour from the ground to an upper storey of a mill or store, you might place it upon your back and carry it up the stairs. In doing so, you would expend so many foot-pounds of work. Let the sack of flour be 100 lbs., your own weight 150 lbs., and the height to which it is raised be 30 feet. Then the

Work done in elevating the flour = 100 lbs. × 30′ = 3000 ft. lbs. × 30' = 4500

99

99

yourself = 150 "

Or, your percentage efficiency would be found from the proportion

In other words, 60 per cent. of the total work done is lost work, and only 40 per cent. is useful work.

If instead of carrying the sack upstairs, you found ready to hand a long rope (with its two ends close to the ground) that had been passed over a smooth iron hook fixed to the outside wall above an outside landing for the particular storey of the building, and, if you attached one end of this rope to the sack and found that by pulling with all your strength (or say with a force of 150 lbs., i.e., equal to your weight) on the other end, you could just lift the sack. Then, if by this means you elevated the sack to the landing, you would have expended less work than by the former method; for,

Pull - Ta-Ts

Ta

Hence 33.3 per cent., or of the total work put in by you in pulling at one side of the rope, is spent in overcoming the friction between the rope and the hook and bending the rope over the hook, whilst only 66.6 per cent., or 3, remain for elevating the sack of flour.

If, instead of the iron hook you had found a double-flanged deep V-grooved pulley with a rope over it, as in the accompanying illustration, and that this pulley revolved so easily on its bearings that you had only to pull with a constant force of 110 lbs. in order to lift the sack of flour from the ground up to the 30-feet level, then

PULLEY AND WEIGHTS.

Work done in elevating flour = 100 lbs. × 30′ = 3000 ft.-lbs. against friction, &c. = IO

× 30' = 300

Total work done

... Mechanical efficiency=

Hence only 9.1 per cent. of the total work put in is lost work in overcoming friction at the pulley bearing and in bending the rope over the pulley.

You see, therefore, what a useful machine a pulley is, not only for enabling you to change the direction of a force, but also for the saving of labour.

A pulley is simply a wheel and axle wherein their radii are one and the same, or a lever with equal arms. Hence the principles of moments and of work may be applied to it in the same way as we applied them to the lever and to the wheel and axle.

Snatch Block.-If you should require to put the bend of a rope on a pulley, and at the same time prevent the possibility of the rope coming out of the groove, without having to reeve the end of the rope between its cheeks, you would use what is called a snatch block. One form of snatch block is illustrated by the accompanying figure, where on the side of one cheek there is a sneck or snatch, which is turned to one side, to enable the bend of the rope to be placed around the U groove of the pulley. The snatch then falls down and closes upon the central pin. Another form has a hinged snatch which can be lifted up at right angles to the face of the cheek, and after the rope has been put on the pulley the snatch is closed down and locked by a pin attached to a short chain fixed to the side of the cheek, just like an ordinary front hinge for closing a chest. The single movable pulley, which is used for supporting the load to be lifted by a Chinese windlass or by a jib crane, is sometimes called a saatch block (see the illustration of the wheel and compound axle in next Lecture, and of jib cranes in Lectures VIII. and XIII.). In the latter case the chain passes from the barrel of the crane over the pulley at the point of the jib, then vertically down, underneath the snatch-block pulley, and vertically upwards to a point on the under side of the jib where it is fixe by an eye-shackle with a bolt and nut. If the load, including the weight of the snatch-block, be W, then, neglecting friction, the pull P on the chain will be ; for W is supported by two vertical or parallel parts of the chain, each part carrying half the load, or W = 2P. If the load be elevated any distance L, then the chain will have to be pulled in on the barrel a distance of 2L, for by the principle of work

Or,

W

2

SNATCH BLOCK.

the load its distance.
W x L.

The theoretical advantage is therefore 2 to 1, or a certain force would lift double the weight, neglecting friction.

Block and Tackle.-Passing over the various arrangements of pulleys for lifting weights which are treated of in theoretical

E

mechanics, we come to this well-known and useful contrivance. As will be seen from the accompanying sketch, it consists of a number of pulleys (or sheaves as they are technically termed) free

BLOCK AND TACKLE.

to run round on a turned central iron or steel spindle, and inserted in a block, having their iron divisions between each pulley, and strong iron cheeks fixed to a swivel joint terminating in an iron hook hung from an eye bolt. Three sheaves are shown in this block, but the number may range from one upwards, according to the size and work to be done. There is a similarly constructed block with two sheaves, from which the weight to be raised, or the body to be pulled, is attached, and this is called the movable block, whereas the upper or home one is termed the fixed block. Around the pulleys of both blocks there is reeved a rope with the inner end made fast to an eye on the movable block, whilst the free end hangs from one of the outside sheaves; but this arrangement is frequently reversed, for the inner end of the rope may be attached to an eye on the fixed block, and the free end may spring from the other one (see the figure in connection with Example I. of this Lecture). The free end of the rope is then ready to be pulled by the hands or by aid of a winch.

Now, neglecting friction, and supposing the rope to be perfectly flexible, a force, P, applied to the free end of the rope would be transmitted throughout it to the other end at the movable block. Hence the effect of this force in overcoming a resistance, W, is multiplied by the number, n, of parts of the rope which spring from the movable block.

(2) The velocity ratio, or ratio of the distance through which P acts, to that through which W is overcome in the same time.

In the figure there are shown

three pulleys in the upper block and two in the lower, with five parts of rope springing from the latter; therefore in this case n

Here

=

5.

since P must pass through five times the distance that W does in the same time.

The velocity ratio

=

P's distance
W's distance

n 5
I 1

So that the theoretical advantage and the velocity ratio have the same algebraical expression and numerical value. (See note, p. 68.) The Principle of Work applied to the Block and Tackle. -Using the very kind of block and tackle represented by the previous figure, atta h a light Salter's spring balance by its hook to the rope where the hand is shown. Fix such a weight to the lower block that the weight of rope between the blocks, the movable block, and the load are 60 lbs. Call this W. Now pull the ring of the spring balance until the load rises slowly and uniformly, and note the reading on the balance; let it be 18 lbs., and let the weight of this balance and the hanging free end of the rope, which is assisting the arm, be 2 lbs. Call this total pull of 20 lbs. P; then :

(3) The actual or working advantage=weight raised_W_60 lbs. __3 pull applied P 20 lbs. 1 Lift W up through one foot exactly, and measure the length of rope which you have pulled out from the upper block, and you will find that it is five feet; hence,*

In the same way the efficiency of any other block and tackle may be found, and the student should carry out a series of

*The above results were obtained by the Author from a block and tackle of the same kind as that shown by the previous figure, at a demon. stration in his Junior Applied Mechanics class.