Part 24 (1/2)

A _bevel gear_ is frequently used to change the direction of the force.

(See Fig. 94.)

[Ill.u.s.tration: FIG. 96.--A single movable pulley.]

[Ill.u.s.tration: FIG. 97.--Block and tackle.]

[Ill.u.s.tration: FIG. 98.--The fixed pulley considered as a lever.]

[Ill.u.s.tration: FIG. 99.--The movable pulley considered as a lever.]

=125. The Pulley.=--The _pulley_ consists of a wheel turning on an axis in a frame. The wheel is called a sheave and the frame a block. The rim may be smooth or grooved. The grooved rim is used to hold a cord or rope. One use of the pulley is to change the _direction_ of the acting force as in Fig. 84, where pulley _B_ changes a horizontal pull at _H_ to a downward force and pulley _A_ changes this into an upward force lifting the weight _W_. These pulleys are fixed and simply change the direction. Without considering the loss by friction, the pull at _W_ will equal that at _F_. Sometimes, a pulley is attached to the weight and is lifted with it. It is then called a _movable pulley_. In Fig. 96 the _movable pulley_ is at _P_, a fixed pulley is at _F_. When _fixed pulleys_ are used, a single cord runs through from the weight to the effort, so that if a force of 100 lbs. is applied by the effort the same force is received at the weight. But with movable pulleys several sections of cord may extend upward from the weight each with the force of the effort upon it. By this arrangement, a weight several times larger than the effort can be lifted. Fig. 97 represents what is called a _block and tackle_. If a force of 50 lbs. is exerted at _F_, each section of the rope will have the same tension and hence the six sections of the rope will support 300 lbs. weight. The _mechanical advantage of the pulley_ or the _ratio of the weight_ to the effort, therefore, _equals the number of sections of cord supporting the weight_. The fixed pulley represents a lever, see Fig. 98, where the effort and weight are equal. In the movable pulley, the fulcrum (see Fig. 99) is at _D_; the weight, _W_, is applied at the center of the pulley and the effort at _F_. The weight distance, _D_{w}_, is the radius, and the effort distance, _D_{f}_, is the diameter of the pulley. Since _W/F = D_{f} / D_{w} = 2_ in a movable pulley, the weight is twice the effort, or its mechanical advantage is 2.

Important Topics

1. Wheel and Axle, Law of Wheel and Axle.

2. Pulley, Fixed and Movable, Block and Tackle, Law of Pulley.

Exercises

1. Why do door k.n.o.bs make it easier to unlatch doors? What simple machine do they represent? Explain.

2. What combination of pulleys will enable a 160-lb. man to raise a 900-lb. piano?

3. When you pull a nail with an ordinary claw hammer, what is the effort arm? the resistance arm?

4. How much work is done by the machine in problem 2 in lifting the piano 20 ft.? How much work must be done upon the machine to do this work?

5. The pilot wheel of a boat has a diameter of 60 in.; the diameter of the axle is 6 in. If the resistance is 175 lbs., what force must be applied to the wheel?

6. Four men raise an anchor weighing {1 1/2} tons, with a capstan (see Fig. 110) having a barrel 9 in. in diameter. The circle described by the hand-spikes is {13 1/2} ft. in diameter. How much force must each man exert?

[Ill.u.s.tration: FIG. 100.--The Capstan.]

7. A bicycle has a 28-in. wheel. The rear sprocket is 3 in. in diameter,[H] the radius of the pedal crank is 7 in.; 24 lbs. applied to the pedal gives what force on the rim of the wheel? What will be the speed of the rim when the pedal makes one revolution a second?

[H] Consider the diameter of the front sprocket as 6 inches.

8. Measure the diameters of the large and small pulleys on the sewing-machine at your home. What mechanical advantage in number of revolutions does it give? Verify your computation by turning the wheel and counting the revolutions.

9. What force is required with a single fixed pulley to raise a weight of 200 lbs.? How far will the effort move in raising the weight 10 ft.?

What is the mechanical advantage?

10. In the above problem subst.i.tute a single movable pulley for the fixed pulley and answer the same questions.

11. What is the smallest number of pulleys required to lift a weight of 600 lbs. with a force of 120 lbs.? How should they be arranged?

12. A derrick in lifting a safe weighing 2 tons uses a system of pulleys employing 3 sections of rope. What is the force required?