114 WELLS'S NATURAL PHILOSOPHY. 



PRACTICAL PROBLEMS IN MECHANICS. 



1. What must be the horse-power of a locomotive engine which moves at the constant 

 Bpced of '25 miles per hour, on a level track, the weight of the train being 60 tons, and the 

 resistance from friction being equal to 430 pounds ? "^ W ^' - 



2. If a lever, twelve feet long, have its fulcrum 4 feet from the weight at one end, and 

 this weight be 12 pounds, what power at the other end will balance? 



3. In a lever of the first class a power of 20 at one end balances a weight of 100 at the 

 other : what is the comparative length of the two arms ? 



4. In a lever of the first class, 6 feet in length, the power is 75, and the weight 150 

 pounds : where must the fulcrum be placed in order that the two may balance 1 



5. Two persons carry a weight of -00 pounds suspended from a pole 10 feet long; one 

 of them being weak can carry only 75 pounds, leaving the rest of the load to be carried 

 by the other : how far from the end of the pole must the weight be suspended ? 



6. A lever of the second class is 20 feet long : at what distance from the fulcrum must 

 a weight of SO pounds be placed in order that it may be sustained by a power of 60 

 pounds ? 



7. In a lever of the third class, 8 feet long, what power will be required to balance a, 

 weight of 100 pounds, the power being applied at a distance of 2 feet from the fulcrum ? 



8. A power of 5 pounds is required to lift a weight of 20, by means of the wheel and 

 axle: what must be the proportionate diameters of the wheel and axle? 



9. A power of 60 acts on a wheel 8 feet in diameter : what weight Buspended from a 

 rope winding round an axle 10 inches in diameter will balance this power? 



10 In a set of cog-wheels the diameters of wheel and axle are, first T and 2, 

 Gccond 8 and 1, third 9 and 1 : a power of 25 being applied at the circumference of the 

 first wheel, what weight will be sustained at the axle of the third ? 



11. What weight will a power of 3 sustain with a system of 4 movable pulleys, one 

 cord passing round all of them ? 



12. Suppose a power of 100 pounds applied to a set of 2 movable pulleys, what weight 

 will it sustain, allowing a deduction of two thirds for friction ? 



13. If a man is able to draw a weight of 200 pounds up a perpendicular wall 10 feet 

 high, how much will he be able to draw up a plank 40 feet long, sloping from the top of 

 the wall to the ground, no allowance bei:ig made for friction ? 



Solution. — In this the height (10) is to the length (40) as the weight (200) is to the re- 

 quired weight. 



14. If a man has just strength enough to lift a cask weighing 106 pounds perpendicu- 

 larly into a wagon .3 feet high, what weight could he raise by means of a plank 10 feet 

 long, with one end resting upon the wagon, and the other on the ground? 



15. The length of a plane is 12 feet, the height is 4 feet : what is the proportion of tha 

 power to the weight to be raised ? 



16. The distance between the threads of a screw beinc; half an inch, and the circumfer- 

 ence described by the power 10 feet, wh»t proportion will exist between the power and 

 the weight ? 



Sol'Uion. — The power will be to the weight as h;ilf an inch, the distance between the 

 threads, is to 10 feet (240 half inches), the circumference described by the power =1 to 240. 



17. A power of 20 pounds acting at the end of a lever attached to a screw describes a 

 circle of 100 inches: whnt resistance will the power overcome, the distance between the 

 threads of the screw being 2 inches ? 



