Now (ft. radius of gyration)2 = (ft. radius of disc.)2, gft.2 (ft. radius of gyration)2; ·09 × 182 × 9 × π 8 X lb. by ft.2. i.e., 103 Ec. 6. What is the kinetic energy of the grindstone when revolving at the rate of 15 revolutions per second? 1. A mass of 6 cwt. moves with a velocity of 20 feet per second; how many units of work are stored up in it? 2. Compare the amounts of kinetic energy in a pillow of 20 lbs. which has fallen through one foot vertically, and an ounce bullet moving at 200 feet per second. 3. Find the number of units of work accumulated in a 24-lb. shot leaving the mouth of the gun with a velocity of 1,500 feet per second. 4. A mass of snow, 28 lbs. in weight, falls from the roof of a house to the ground, a distance of 40 feet. Calculate the kinetic energy acquired at the time of impact. 5. A ball weighing five ounces, and moving with a velocity of 1,000 feet per second, strikes a shield, and after piercing it moves on with a velocity of 400 feet per second. How much energy has been expended in piercing the shield? 6. Calculate the kinetic energy of a tram-car weighing 25 tons, when it is moving at the rate of 6 miles an hour, and is laden with 36 passengers, averaging 11 stones each in weight. 7. If the coefficient of kinetic friction for a tram-car moving on its rails is }, find how much work is done when the above car, loaded as stated, is pulled 3 miles along a level road. 8. Calculate the kinetic energy of a hammer of 5 tons let fall half a foot. 9. Two 30-ton hammers moving in opposite directions at 20 feet per second, simultaneously strike a mass of soft iron. How many foot-pounds of work will they do upon it? 10. A 32-lb. ball is thrown vertically upwards with a velocity of 20 feet per second. What is its kinetic energy when it has gone 5 feet? 11. A train of 200 tons starting from rest acquires a velocity of 40 miles an hour in 3 minutes on a horizontal railroad. What is the excess of the moving above the retarding forces, each being assumed uniform? 12. What is the amount of kinetic energy in an engine of 25 tons when moving with a velocity of 20 miles per hour? What force, measured in poundals, acting for ten seconds, is sufficient to stop the engine? 13. What average force will bring to rest in 20 feet a tram-car of 5 tons, having a velocity of 6 miles per hour? 14. Supposing the coefficient of friction to be 0.05, how far will a railway carriage run on level rails with a velocity of 10 miles an hour? 15. If an ounce bullet leaves a gun with a velocity of 800 feet per second, the gun barrel being 3 feet long, what would be the accelerating force on the bullet, supposing it to have been acting uniformly throughout? 16. A bullet weighing 2 ounces leaves a gun with a velocity of 1,550 feet per second; the length of the gun barrel is 2 feet; find the average accelerating force upon the bullet within the barrel, and express it in gravitation units. 17. A shot of 1,000 lbs., moving at 1,600 feet per second, strikes a fixed target; how far will the shot penetrate the target, exerting upon it an average pressure equal to the weight of 12,000 tons? 18. A locomotive of 15 tons, being supposed to acquire a speed of 20 miles an hour in moving through a mile of distance, under the action of a constant difference of moving and resisting forces; calculate in lb. weight the requisite difference of the forces. 19. A heavy body is projected up an incline rising 1 in 100; the friction against the plane is one tenth of the pressure; find the distance it will travel before being reduced to rest, the velocity of projection being 121 feet per second. 20. Find the tension on a rope which draws a carriage of 8 tons up a smooth incline of 1 in 5, and causes an increase of velocity of 3 feet per second per second. 21. If on the same incline the rope breaks when the carriage has a velocity of 48.3 feet per second, how far will the carriage continue to move up the incline? 22. A mass P, after falling freely through h feet, begins to pull up a heavier mass by means of a string passing over a pulley as in Attwood's machine; find the height through which Q will be lifted. 23. Two masses of 5 and 10 lbs. respectively impinge directly, moving with velocities of 8 and 10 feet per second. Find the common velocity after impact, and show that there has been a transformation of kinetic energy. 24. A bullet weighing 50 grammes is fired into a target with a velocity of 500 metres a second. The target is supposed to weigh a kilogramme, and to be free to move. Find in kilogrammetres the loss of energy in the impact. 25. An ounce-bullet leaves the mouth of a rifle with a velocity of 1,500 ft. per sec. If the barrel be 4 ft. long, calculate the mean pressure of the powder, neglecting all friction. 26. The bob of a simple pendulum is pulled through an arc of 60 degrees, and let go. Compare its kinetic energy after describing an arc of 30 degrees with its energy at the lowest point. 27. Find the initial velocity of a shot of 1,000 lbs. discharged from a 100-ton gun, supposing none of the 30,000 foot-tons of energy given out by the explosion to be wasted in heat, light, or sound. 28. A cannon-ball of 5 kgm. is discharged with a velocity of 500 metres per second; find its kinetic energy in ergs. If the cannon be freely suspended, and have a mass of 100 kgm., find in ergs the energy of the recoil. 29. The moment of inertia of a ring is 50 kilogramme by (metre)2; what is it in terms of pound by (foot)2? 30. A fly-wheel has a mass of 30 tons, which may be supposed to be distributed along the circumference of a circle 8 feet in radius; it makes 20 revolutions per minute; find its kinetic energy in foot-pounds. 31. What is the kinetic energy of a circular saw having a diameter of 2 feet, and inch thick, when moving with a circumferential velocity of 6,000 feet per minute? The density of steel is 500 lb. per cubic foot. 32. The rim of a fly-wheel, specific gravity 7.75, whose inner and outer radii are 4 and 5 feet respectively, and whose thickness is 1 foot, revolves uniformly 20 times per minute round its axis; calculate in foot-pounds the entire amount of work accumulated in it. 33. A cord, which may be taken as weightless, is wrapped round the circumference of a wheel of 3 feet radius, and a weight of 14 lbs. is attached to the free end of the cord. The mass of the wheel is 300 lbs., and its radius of gyration about the axis is 2 feet. The weight being let go from rest falls for 2 seconds; find how far it has fallen, and its velocity at the end of that time. There is supposed to be no friction. 34. A mass of 10 lbs. is attached by a string to the rim of a circular disc, the mass of which is 25 lbs., and the radius of gyration 13 feet. Find the angular velocity of the disc 5 seconds after the weight is allowed to fall, supposing that there is no friction. 35. A uniform circular cylinder of 100 lbs. mass and one foot radius revolves frictionlessly on its axis, which is horizontal. A thread rolled round the cylinder carries on one end, which hangs down freely, a weight of one lb. Find how far the weight falls from rest in 3 seconds. 36. A rod of uniform density, which can turn freely round one end, is let fall from a horizontal position; what is its angular velocity when it reaches its lowest position? SECTION XXXV.-POWER. ART. 162.-Power. By power is meant the rate at which work is done by an agent. It is expressed in terms of W per T. The term activity is used by Sir W. Thomson and Professor Tait to denote this idea. The British absolute unit is the foot-poundal per second, and the C.G.S. unit is the erg per second. Gravitation units are footpound per sec., kilogrammetre per minute, etc. A practical unit is the horse-power, founded by Watt on an estimate of the average rate at which a horse can work; 1 horse-power = 33,000 foot-pounds per minute, 550 foot-pounds per second. The intensity of gravity is taken at its standard value. The corresponding French unit is the force de cheval ; 1 force de cheval = 75 kilogrammetres per second. It has recently been proposed to introduce the term "watt" to denote 107 erg per sec., which is a convenient unit of power in clectrical measurements. EXAMPLES. Ex. 1. Calculate the amount of work done against gravity in drawing a car of 2.5 tons, laden with 30 passengers averaging 11 stones each, up an incline, the ends of which differ in level by 120 feet. Also, find the horse-power sufficient to do that work in half an hour. (2.5 × 20 × 112 + 30 × 11 × 14) lb. weight, and 120 feet height, .. (2·5 × 20 × 112 + 30 × 11 × 14) 120 foot-pounds, .. i.e., 1,226,400 foot-pounds. 1 horse-power = 33,000 foot-pounds per minute, 1 horse-power = 33,000 × 30 foot-pounds; Ex. 2. Express a horse-power in terms of the C.G.S. absolute unit. Now 33,000 foot-pounds per minute, i.., 33,000 lb. by weight by foot per minute. |