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MECHANICS

Mechanics treats of forces and of the effects of forces. Force is the action between two bodies tending to produce a change of position or shape; as when a horse pulls a load, a motor drives an electric car, elasticity causes the action of a steel spring, etc.

The moment of a force. If a bar of uniform size is pivoted at its center and a weight placed on one end, the bar will rotate about the pivot. The numerical value of the importance of the force in producing motion about a pivot is called its moment and is equal to the product of the force by the distance from its line of action to the pivot. By reference to the accompanying sketch, the moment of the force F1, applied at point A, is seen to be 6×10=60 ft.-lbs. of F2, 4×10=45 ft.-lbs.

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When a force acting upon a body changes its position,

work is done upon the body. The amount of work done

depends upon the force applied, also upon the distance through which it acts; that is, work is measured by the resistance overcome, multiplied by the distance through which it is overcome; as a 10 pound weight that is lifted to a height of 5 feet requires an amount of work equal to the product of 10 times 5-50 ft.-lbs.

The unit of measure in the above example is expressed by the term foot-pound, that is, a force of one pound acting through a distance of one foot, or its equivalent; as 4 pounds acting through a distance of foot, or 1 pound acting through 10 feet, etc.

The unit can be expressed not only in ft-lbs. but in inchpounds, foot-tons, centimeter-grams,* etc.

The amount of work done in lifting a body a given distance is the same whether done in 5 seconds or 5 minutes, but it is often necessary also to denote the rate of doing work.

This is expressed in terms of horse power. An engine of one horse power (1 H. P.) means an engine capable of doing 33,000 ft.-lbs. of work in one minute.

Therefore to find the horse power of any machine the formula used is,

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In electric power machines such as dynamos and motors one H. P. is equal to 746 watts; then the formula for power of electric machines is:

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Energy is the capacity for doing work; as a coiled spring has the capacity to set in motion the mechanism of a clock

*Note. For dimensions in the metric system see tables, pages 173 to 176.

or watch. The coiled spring of a watch possesses energy because at some previous time work has been performed upon it in the winding.

The amount of energy in a body is measured in ft.-lbs., the unit used for measuring work. Mechanical energy is of two kinds, potential, and kinetic. Potential energy is due to the position of a body; as, for example, if a pile driver head weighing 50 pounds is suspended 20 feet above the ground it has a potential energy of 20×50=1000 ft.-lbs. If now the weight is released and falls, the energy is of a different kind because of the motion of the falling weight. This is called kinetic energy. In either case the weight times the height equals the measure of the energy of the body or K-Wh.

When the velocity of the falling body is given instead of the height from which it falls,

Then by the laws of falling bodies

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A drop hammer weighing 400 lbs. falls from a height of 36 in. What kind and how much energy will be exerted? 2. A weight of 500 lbs. is used for breaking up old car wheels and is suspended 15 ft. above the anvil block. Calculate the kind and amount of energy.

3. An elevator car weighing 2 tons requires how much energy to lift it a distance of 20 feet?

4. A tank contains 5,000 gals. of water, 50 ft. being the average height above the ground. What is the energy of the water at the ground?

5. A pile driver head weighing 175 lbs. falls from a height of 18 ft. What is the energy at the end of the fall? 6. A man weighing 180 lbs. jumps up to a platform 42 inches above the ground. How much energy was expended?

7. If the man in problem 6 should climb a distance of 100 ft. above a certain point, how much energy would be exerted?

8. If a hammer that weighs 1 lb. has a velocity of 22 ft. per sec., what is its energy?

9. If an iron ball weighs 100 lbs., what is its energy when suspended at a height of 28 ft. from the ground? 10. A rock drill is operated by a 10 lb. sledge hammer with a striking velocity of 30 ft. per sec. Find the energy

used in the drilling.

11. What is the H. P. of a pump that raises 100,000 gals. of water per hour to a reservoir 25 ft. above the level of the lake from which it is pumped?

Note. One cu. ft. of water weighs approximately 62 lbs. and contains about 7 gals.

12. A motor is able to lift an elevator, which with load weighs 5 tons, to the top of a tower 500 ft. high in two minutes. What H. P. is required to do the work?

13. What must be the H. P. of the engine required to raise a block of granite weighing 10 tons to the top of a wall 35 ft. from starting point when it takes 20 minutes to do the work?

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