14. A glass flask contains, when full at 9° C., 100 cub. cm. of mercury. The coefficient of cubical expansion of glass being 0.000026, and that of mercury 0.00018, find the volume at 100° C. of the mercury driven out when the flask and mercury are heated to 100°. 15. Three separate mixtures are made, namely— (1) Water and snow, (2) Water and salt, If all the materials were, before being mixed, at 0° C., which mixture will be at the highest temperature and which at the lowest? and why? 16. A glass bottle and a bottle of porous earthenware are both filled with water and exposed to the air side by side. Usually, the water in the earthenware bottle becomes decidedly colder than that in the glass; why is this? If there is little or no difference of temperature, what conclusion may we draw as to the state of the atmosphere? and why? ANSWERS TO THE NATURAL PHILOSOPHY PAPER. 1.-(i) The body must have an initial velocity independent of the forces. (ii) The resultant of the forces must be 0. 2. The second component may be found by drawing AB vertically upwards, containing 20 units of length, and AC horizontally containing 10 units. Join BC and through A and B draw AD and BD parallel respectively to BC and AC. AD will represent the second component. AD AB2 + BD2 =400 + 100 = 500 .*. AD = 10/5. 3.-(i) Suppose the stick to rest in such a position that the bundle and his hand are at equal distances from his shoulder, then the force required to maintain equilibrium is just equal to the weight of the bundle. The pressure on his shoulder is now double the weight of the bundle. (ii) Suppose the bundle to be shifted nearer to his shoulder. A smaller force is now required to maintain equilibrium, and the pressure on his shoulder is consequently less than double the weight of the bundle. (iii) If the bundle be shifted further away from his shoulder the force required to maintain equilibrium is greater, and the pressure on his shoulder is more than double the weight of the bundle. 4. The single force must be equal to the sums of 5, 6, 9, and 7 lbs., that is, 27lbs. Take moments about the edge which sustains the 7 and 9 lb. weights. 27 x 11 x 27 x = 11. The force must be applied 11 inches from this edge. Take moments about the edge sustaining the 6 and 9lb weights. 27 y 12 x 27 The force must be 12 inches from the second edge. 5. Acceleration is the rate of change of velocity. Let F be the moving force, and a the acceleration, and m the mass moved. Then F ma. 6.- -(i) The velocity after passing the ring is (with the same masses) found to be always proportional to the time of motion before reaching the ring; which, of course, proves that the acceleration must have been constant. (ii) Always taking the total sum of the three masses constant, but varying the unequal mass, and keeping constant the time of motion before reaching the ring, the velocity after passing the ring is found to be proportional to the unequal mass; which proves that the acceleration is also proportional to this mass, which is the mass acting on the system. 7. A velocity of 15 miles per hour is 22 feet per second. But if the pull of the engine be F and M the mass of the train— The weight of any substance in grammes is found by multiplying its volume in cubic centimetres by its density. The numerator is proportional to the weight of a certain volume of alcohol, and the denominator to the weight of the same volume of water; so it is only necessary to divide one by the other to obtain the required specific gravity. 10. The condensing pump consists of a cylindrical barrel with a valve at the bottom opening downwards into a vessel called the receiver. A piston with a valve, opening downwards, works in the barrel. At each stroke 80 cubic centimetres are forced into the receiver. After 38 strokes the receiver will contain above 4000 cubic centimetres condensed into the space of 1000, and the pressure will be consequently increased fourfold. 11. If we measure equal lengths along the two portions of a ray of light refracted from air into water, and from the extremities of these equal lengths draw perpendiculars to the normal to the surface at the point of incidence, the ratio of these perpendiculars will be found to be, that beneath the surface of the water being the shorter. Index of refraction of turpentine with respect to air = 1,0 × 3/ = 1·481. 12. In each case the candle and its image are placed at a pair of conjugate foci of the lens; and since the distance between the object and the image remains constant, these pairs of conjugate foci must lie symmetrically with regard to the lens, i. e., when the lens is 1 foot from the candle it is 11 feet from the wall, and when it is 11 feet from the candle it is 1 foot from the wall. 13. 200 c. c. of water in falling from 99° C. to 57° C. give up 200 × 42 units of heat. 200 c. c. (= 206 grams) of milk in rising from 15° C. to 57° C. absorb 206 × 42 × S units, where S is the specific heat of milk. The copper vessel in rising from 15° C. to 57° C. absorbs 8 x 42 units. 200 × 42 = 206 × 42 × S + 8 × 42 14. Since the coefficient of absolute expansion of mercury is '00018, and that of glass is '000036, the coefficient of apparent expansion of mercury in a glass envelope is 00018000026 =000154. 100 c. c. of mercury in being heated from 9° C. to 100° C. will expand 100 X 91 X 000154 c. c. = 1.4014 c. c. 15. Water and snow mixed together at 0° C. preserve the same temperature. A mixture of salt and snow is very much used as a freezing mixture: its power of freezing depends upon the fact that heat is absorbed in the liquefaction of the two solid bodies. With this mixture a temperature of about -20° C. can be obtained for many hours. One gram of salt absorbs 9 units of heat during solution in water, but as each gram requires about 18 grams of water for solution at 0° C. the temperature is only lowered very slightly below 0° C. 16. Water gradually soaks through the porous earthenware and evaporates on its outer surface: during the process of evaporation heat is absorbed from the bottle and its contents; the temperature consequently sinks below that of the glass bottle, from which there has been no evaporation. If there is little or no difference in the temperature, we may assume that no evaporation is taking place owing to the fact that the surrounding air is nearly saturated with moisture. LONDON: PRINTED BY C. F. ROWORTH, GREAT NEW STREET, FETTER LANE-E.C. |