34 FORCE AND ENERGY 



Not only water, but all liquids and gases, have this 

 buoyant power. The more dense the liquid or gas, the 

 greater is its power of buoyancy. Hence we may state 

 the facts regarding buoyant force as a general rule : 



A body immersed in a liquid or gas is buoyed up with a 

 force just equal to the weight of the liquid or gas it displaces. 



A floating body sinks into the liquid supporting it until it has pushed 

 aside its own weight of liquid. Thus a piece of cork % as dense as 

 water sinks until % of its volume is below water. A piece of ice 0.92 

 as heavy as water has 0.92 of its volume below water. 



A needle (cf. 31) has really a much greater density than water, 

 but it can be supported on water because its weight is very small. As 

 a result the elastic surface of the water does not break. If the needle 

 becomes wet, the water surface breaks, and the needle sinks. 



35. Center of Mass. Why does a slender stick 

 which has been set upright fall over so easily? Why 

 cannot we stand an egg "on end"? The answer is 

 found in a study of the center of mass of a body. 

 We all know what is meant by the center of a sphere: 

 it is the point around which the volume of the 

 sphere is arranged in a regular way. Let us call this cen- 

 ter the center of volume of the sphere. Now, in a wooden 

 ball or a lead ball the matter, as well as the volume, is all 

 grouped around the center; so we can call the center of 

 volume the center of mass, or center of gravity, of the ball. 



If we were to mix small fragments of lead and sawdust 

 uniformly together, and pack them into a ball, the center 

 of mass of the ball would still be the same as its center of 

 volume. But if we were to make half of the ball of wood 

 and the other half of lead, and were to fasten the two 



