Physics Part 25

1. Efficiency of machines.

2. The inclined plane, wedge and screw. Applications.

Exercises

1. A plank 12 ft. long is used to roll a barrel weighing 200 lbs. into a wagon 3 ft. high. Find the force required parallel to the incline.

2. How long a plank will be needed to roll an iron safe weighing 1-1/2 tons into a wagon 3 ft. high using a pull of 600 lbs. parallel to the incline.

3. An effort of 50 lbs. acting parallel to the plane prevents a 200-lb.

barrel from rolling down an inclined plane. What is the ratio of the length to the height of the plane?

4. A man can push with a force of 150 lbs. and wishes to raise a box weighing 1200 lbs. into a cart 3 ft. high. How long a plank must he use?

5. The radius of the wheel of a letter press is 6 in., the pitch of its screw is 1/4 in. What pressure is produced by a force of 40 lbs.?

6. The pitch of a screw of a vice is 1/4 in., the handle is 1 ft. long.

what pressure can be expected if the force used is 100 lbs.?

7. A jackscrew is used to raise a weight of 2 tons. The bar of the jackscrew extends 2 ft. from the center of the screw. There are two threads to the inch. Find the force required.

(6) FRICTION, ITS USES AND LAWS

=130. Friction.=--Although often inconvenient and expensive, requiring persistent and elaborate efforts to reduce it to a minimum, friction has its uses, and advantages. Were it not for friction between our shoes and the floor or sidewalk, we could not keep our footing. _Friction is the resistance that must be overcome when one body moves over another._ It is of two kinds, _sliding_ and _rolling_. If one draws a block and then a car of equal weight along a board, the force employed in each case being measured by a spring balance, a large difference in the force required will be noticed, showing how much less rolling friction is than sliding friction.

=131. Ways of Reducing Friction.=--(a) Friction is often caused by the minute projections of one surface sinking into the depressions of the other surface as one moves over the other. It follows, therefore, that if these projections could be made as small as possible that friction would be lessened. Consequently _polis.h.i.+ng_ is one of the best means for reducing friction. In machines all moving surfaces are made as smooth as possible. In different kinds of materials these little ridges and depressions are differently arranged. (b) In Fig. 109 the friction between _R_ and _S_ would be greater than between _R_ and _T_. In _R_ and _S_ the surfaces will fit closer together than in _R_ and _T_. The _use of different materials will reduce friction_. The iron axles of car wheels revolve in bearings of bra.s.s. Jewels are used in watches for the same reason. (c) Another very common method of reducing friction is by the use of _lubricants_. The oil or grease used fills up the irregularities of the bearing surfaces and separates them. _Rolling friction_ is frequently subst.i.tuted for sliding friction by the use of ball and roller bearings. These are used in many machines as in bicycles, automobiles, sewing machines, etc. (See Fig. 110.)

[Ill.u.s.tration: FIG. 109.--The friction between _R_ and _S_ is greater than between _R_ and _T_.]

=132. Value of Friction.=--_Friction always hinders motion_ and whenever one body moves over or through another the energy used in overcoming the friction is transformed into heat which is taken up by surrounding bodies and usually lost. Friction is therefore the great obstacle to perfect efficiency in machines. Friction, however, like most afflictions _has its uses_. We would find it hard to get along without it. Without friction we could neither walk nor run; no machines could be run by belts; railroad trains, street cars, in fact all ordinary means of travel would be impossible, since these depend upon friction between the moving power and the road for propulsion.

[Ill.u.s.tration: FIG. 110.--Timken roller bearings. As used in the front wheel of an automobile.]

=133. Coefficient of Friction.=--The ratio between the friction when motion is just starting and the force pus.h.i.+ng the surfaces together is called the _coefficient of friction_.

If the block in Fig. 111 is drawn along the board with uniform motion, the reading of the spring balances indicates the amount of friction.

Suppose the friction is found to be 500 g., and the weight of the block to be 2000 g. Then the coefficient of friction for these two substances will be {500/2000} = {1/4}, or 25 per cent.

=134. Laws of Friction, Law I.=--_The friction when motion is occurring between two surfaces is proportional to the force holding them together._ Thus if one measures the friction when a brick is drawn along a board, he will find that it is doubled if a second brick is placed on the first. On brakes greater pressure causes greater friction. If a rope is drawn through the hands more pressure makes more friction.

[Ill.u.s.tration: FIG. 111.--A method for testing the friction between surfaces.]

=Law II.=--_Friction is independent of the extent of surface in contact._ Thus a brick has the same friction drawn on its side as on its edge, since, although the surface is increased, the weight is unchanged.

=Law III.=--Friction is greatest at starting, but after starting is practically the same for all speeds.

=135. Fluid Friction.=--When a solid moves through a fluid, as when a s.h.i.+p moves through the water or railroad trains through the air, the resistance encountered is not the same as with solids but increases with the square of the velocity for slow speeds and for high speeds at a higher rate. This is the reason why it costs so much to increase the speed of a fast train, since the resistance of the air becomes the prominent factor at high speeds. The resistance to the motion of a s.h.i.+p at high speed is usually considered to increase as the cube of the velocity so that to double the speed of a boat its driving force must be eight times as great.

Important Topics

1. Friction: two kinds; sliding and rolling.

2. Four ways of reducing friction.

3. Uses of friction.

4. Coefficient of friction. Three laws of friction.

5. Fluid friction.

Exercises

1. How long must an inclined plane be which is 10 meters high to enable a car weighing 2000 kg. to be pushed up its length by a force of 100 kg.

parallel to the incline?

2. State how and where friction is of use in the operation of the inclined plane, the wedge, the screw, the wheel and axle.

3. A wheelbarrow has handles 6 ft. long. If a load of 300 lbs. is placed 18 in. from the axis of the wheel, what force placed at the end of the handles will be required to lift it?

4. A jackscrew has 3 threads to the inch, and the lever used to turn it is 4 ft. long. If the efficiency of the screw is 60 per cent., what force must be applied to raise a load of 5 tons?

5. In problem 4 how far must the force move in raising the weight 3 in.

Compute the work done upon the weight, the work done by the power and the efficiency of the machine from these two amounts of work.

6. What simple machines are represented in a jackknife, a sewing-machine, a screw-driver, a plane, a saw, a table fork?

7. A laborer carries 1500 lbs. of brick to a platform 40 ft. high. How much useful work does he do?

8. If he weighs 150 lbs. and his hod weighs 10 lbs., how much useless work does he do in taking 30 trips to carry up the bricks of problem 7?

What is his efficiency?

9. If the laborer hoists the brick of problem 7 in a bucket weighing 50 lbs., using a fixed pulley and rope, what is the useless work done if it takes 12 trips to carry up the brick? What is the efficiency of the device?

10. The efficiency of a set of pulleys is 70 per cent. How much force should be applied if acting through 100 ft. it is to raise a load of 400 lbs. 20 ft.?

11. The spokes of the pilot wheel of a motor-boat are 1 ft. long, the axle around which the rudder ropes are wound is 3 in. in diameter. What effort must be applied if the tension in the ropes is 50 lbs.?

12. Why are the elevated railway stations frequently placed at the top of an incline, the tracks sloping gently away in both directions?

13. The screw of a press has 4 threads to the inch and is worked by a lever of such length that an effort of 25 lbs. produces a force of 2 tons. What is the length of the lever?

14. It takes a horizontal force of 10 lbs. to draw a sled weighing 50 lbs. along a horizontal surface. What is the coefficient of friction?

15. The coefficient of rolling friction of a railroad train on a track is 0.009. What pull would an engine have to exert to haul a train weighing 1000 tons along a level track?