Physics 110 Homework SolutionsChapter 13

(1) Force is defined as that quantity that causes a change in motion. It is a push or a pull on abody. Of course, a force need not cause motion; it may be applied to the body along with otherforces that balance producing a vanishing net force on the body. A fluid applies a force to itscontainer. The force it applies depends on the geometry of the container, that is, its size andshape. We want to define a force like quantity that is independent of the size and shape of thecontainer. This quantity is the pressure and is defined to be the force applied by the fluiddivided by the area over which the force is applied. Note that force is a vector, while pressure isa scalar. In fact, pressure in a fluid away from a wall acts in all directions at once.

(2) As anyone who has swum to the bottom of a swimming pool can attest, pressure increaseswith depth. In fact, the pressure in a fluid due to the fluid is proportional to the depth. Thepressure at a point in a fluid is due to the weight of the fluid above that point, which is propor-tional to the mass of the fluid above the point. The mass is proportional to the density of thefluid. Thus, the pressure in a fluid due to the fluid is proportional to the density of the fluid.

(3) If a 1-L container is submerged half way in water, then half of its volume displaces water.Thus, the volume of the displaced water is The buoyant force on the container will be equalto the weight of the displaced water, which is the weight of a half a liter of water. One liter ofwater has a mass of 1 kg, so a half a liter has a mass of Multiplying by g = 9.8 m/s gives2

the weight of the displaced water, which is 4.9 N.

(4) It is the pressure exerted by the knife that determines how well it cuts. Since the area overwhich the force is applied is smaller for a sharp knife than a dull one, the pressure applied bythe sharp knife will be greater than that applied by the dull knife. The sharp knife cuts moreeasily.

(5) When the iron weight is placed on the block, the block must sink into the water to increasethe buoyant force. The total volume displaced must be the same whether the weight is placedon top of the block or hung below it. But, if it is hung below it, the volume of the iron accountsfor part of this volume, which means that the block need not sink as far into the water in thiscase.

(6) The density of a mixture of two substances must have a value between the densities of thetwo substances. Thus, a mixture of water and alcohol will have a relative density between the0.8 of alcohol and the 1 of water. The mixture will have a density less than 1, which means thatthe ice will float lower in the combination than it does in water alone. The more alcohol thereis, the lower the density will be. If there are equal amounts of water and alcohol, the relativedensity of the mixture will be 0.9, the same as that of ice. In such a mixture, the ice will floatanywhere in the glass. If there is more alcohol than water in the mixture, the ice will be moredense than the mixture and will sink to the bottom. A cocktail for which this is the case will bestrong one.