1. What power must be applied to the circumference of a wheel 6 ft. in diameter, to balance 350 lbs., suspended from the axle, which is .5 of a foot in diameter ?

Ans. 29 lbs. 23 oz.

2. The diameter of the wheel being 7 ft., and that of the axle being 9 in., what weight will a power equal to 12 lbs. balance? Ans. 112 lbs 3. What must the diameter of a wheel be so that a power equal to 40 lbs. may balance a weight of 500 lbs., the axle being 1 ft. in diameter ? Ans. 12 ft. 4. What must the diameter of the axle be, so that a power equal to 30 lbs. may balance a weight of 270 lbs., the wheel being 9 ft. in diameter ?

Ans. 1 ft.

5. There are 2 axles, side by side, 1 ft. in diameter, each of which has a wheel 10 ft. in diameter; a belt passes round the first axle and the second wheel; how many pounds on the second axle, will a power equal to 25 lbs. on the first wheel balance ? Ans. 2,500 lbs.

6. A wheel is 9 ft. in diameter, and the axle 10.8 in., the power is equal to 38 lbs., and the weight is 310 ĺbs.; which will overcome in this machine, the weight or the power? Ans. The power.

Observations on the Wheel and Axle. When the power and weight balance each other, the power must be increased a little in order to overcome the friction on the axis, and raise the weight; the power may also be diminished a little before the weight will overcome the friction and descend.

The wheel and axle are used in a great many different forms; the crank of the windlass with which water is sometimes drawn, turns round in a circle, and acts as a wheel, while the body of the windlass acts as an axle ; the windlass of a vessel acts as a wheel and axle; the capstan of a vessel is, in effect, a wheel and axle, where the wheel, represented by the levers, is horizontal, &c.

What is said of friction in the wheel and axle ?

Name some of the forms in which the wheel and axle are used?

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.

2. There are 3 movable pulleys, and one end of the rope is attached to the block which contains them; what power will be necessary to balance a weight of 420 lbs.

Ans. 60 lbs. 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. 166 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 increased 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.

LESSON 200.

THE SCREW.

Figure 31.

MM

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?