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 polishing 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 brass. 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 substituted 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.)
