A pulley with an immovable block, like figure 26, is called a fixed pulley. A pulley with a movable block, like figure 27, is called a movable pulley. With one fixed pulley, like figure 26, the power must evidently be 'equal to the weight in order to balance it; this pulley merely serves to change the direction in which the power operates. With one movable pulley, like figure 27, the weight must be 2 times the power in order to be balanced, for the weight is

What is called a fixed pulley? A movable pulley? With one fixed pulley, how is the power to the weight? What does the fixed pulley serve for? With one movable pulley, how is the power to the weight? Why?

supported by 2 ropes. In figure 28, we see that the weight is supported by 4 ropes, and is evidently 4 times the power required to balance it. In figure 29, we see that the weight is supported by 5 ropes, and is evidently 5 times the power required to balance it.

Therefore, to find what weight the power will balance, Multiply it by as many ropes as support the weight.

1. What weight will a power equal to 80 lbs. balance by means of pulleys, the weight being supported by 4 ropes Ans. 320 lbs.

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2. If there are 3 movable pulleys, and one end of the rope is attached to the block which contains them, as in fig. 29; what power will balance a weight of 420 lbs.? Ans. 60 lbs. Explanation. Make a figure on your slate.

3. A system of pulleys support the weight by means of 8 ropes, and the power is applied through an axle, .8 of a foot in diameter, to which there is a wheel 8 feet in diameter; what power at the wheel will balance a weight of 5,000 lbs. Ans. 62 lbs.

Observations on the Pulley. When the power and weight balance each other, the power must be increased in order to raise the weight, of the power being usually lost in overcoming friction; the power may also be diminished about before the weight will overcome the friction and descend.

4. What power operating on pulleys will be necessary to raise a weight of 360 lbs. supported by 6 ropes

? Ans. 90 lbs. 5. What weight will a power equal to 50 lbs. raise by means of 2 movable pulleys, one end of the rope being fastened to the block which contains them?

Ans. 1663 lbs.

6. There is a power equal to 30 lbs. and a weight of 200 lbs.; if one end of the rope is fastened to the block of the fixed pulleys, how many movable pulleys must there be so that the power shall raise the weight?

Ans. 5.

What do we see in figure 28, lesson 198? In figure 29, lesson 198?

What is the rule to find what weight the power will balance?
What is said of friction in the pulley?

A power must be employed, parallel to the plane, which shall be to the weight of the body as the height of the plane is to its length.

1. There is an inclined plane 8 ft. long, and 3 ft. high; what weight will be balanced on it by a stone weighing 12 lbs., acting by means of a line over a fixed pulley, at the top of the plane? Ans. 32 lbs.

2. What power will be necessary to hinder an iron cylinder, weighing 600 lbs., from rolling down a plane, the length of which is 25 ft., and the height 5 ft.?

Ans. 120 lbs. 3. There is a platform 39 ft. long, one end of which is to be raised so that a power equal to 100 lbs. shall just sustain a wagon weighing 975 lbs. on it; how high must the end be raised? Ans. 4 ft.

4. There is an inclined plane, 90 ft. long, and 12 ft. high, on which is a wagon weighing, with its load, 6,000 lbs. ; what power applied through a system of pulleys supporting the weight by 8 ropes, will sustain the wagon on the plane? Ans. 100 lbs.

Observations on the Inclined Plane. When the power and weight balance each other, the power must be increas ed a little, in order to overcome the friction, and cause

If we place a very smooth body on an inclined plane, very smooth and slippery, what do we find?

What is said of friction on an inclined plane?

the weight to move up the plane. The power may also be diminished a little, before the weight will overcome the friction and descend.

The screw consists of two parts, the external screw and the internal screw. The external screw is a cylinder with a spiral projection, called the thread, coiled round it. This thread fits into a groove, cut in the internal screw. The thread is an inclined plane, and operates like one. It rises in passing round the screw the distance between the tops of the coils or turns. When the thread is triangular, this distance is evidently the same as that between the coils. Therefore, in order that the screw may balance the weight and sustain it without turning, we must apply to the thread a power which shall be to the weight as the distance between the tops of the coils is to the length of one -turn or revolution of the thread. Now if the power is applied at the end of a lever, we may imagine the thread to extend to the end of the lever, and then it is obvious that

What does the screw consist of? What is the external screw? Into what does this thread fit? What is the thread, and how does it operate? How much does it rise in passing round the screw? When the thread is triangular, what is this distance the same as? What is necessary in order that a screw may balance the weight and sustain it without turning?

To balance the weight,

The power must be to the weight as the distance between the tops of the coils is to the circumference described by the lever.

1. A certain screw has a triangular thread, the coils of which are 1 inch apart; what weight will be balanced on it by a power equal to 40 lbs., applied at the end of a lever 4 ft. from the centre of the screw?

Ans. 12,063.7 lbs., about.

Note. The circumference described by the lever, in example 1, is a mere trifle more than the circumference of a circle of which the lever is the radius, because the lever rises 1 inch, in turning round.

2. If a screw has a square thread with the tops of the coils of an inch apart, and a lever 36 in. long, what power applied to the lever will balance a weight of 1,500 lbs. ? Ans. 5 lbs. 4 oz, nearly. 3. There is a weight of 7,540 lbs. to be sustained by a to which a power equal to 25 lbs. can be applied by means of a lever 6 ft. long; the thread being square, what distance must the tops of the coils be apart Ans. 1 inch, nearly.

screw,

4. There is a downward pressure of 5,000 lbs. to be exerted by a power equal to 40 lbs., through the medium of a screw having a triangular thread the coils of which are of a ft. apart; how long must the lever be?

Ans. 3.18 ft., about.

Observations on the Screw. When the power balances the weight, the power must be increased in order to raise the weight; of the power being usually lost in overcoming friction. The power may also be diminished about before the weight will overcome the friction and descend.

5. There is a weight of 1,508 lbs. to be raised 5 ft. high by means of a screw which has a lever 5 ft. long, and a square thread with the tops of the coils of an inch apart; what power will be necessary ? Ans. 4 lbs.

6. What weight will a power equal to 35 lbs. raise by means of a screw with a lever 4 ft. long, the thread being triangular, and the coils 13 inch apart?

Ans. 5,277.9 lbs., nearly.

If the power is applied at the end of a lever, what is necessary to bal

ance the weight?

What is said of the friction of the screw?