An Iron Rod 1 of 14 > I Review | Constants V PartA On a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m3 , length 94.6 cm and diameter 3.00 cm from a storage room to a machinist. Calculate the weight of the rod, w. Assume the tree-fall acceleration is g = 9.80 m/s2 . Express your answer numerically in newtons. D View Available Hint(s) Crown of Gold? According to legend, the following challenge led Archimedes to the discovery of his famous principle: Hieron, king of Syracuse, was suspicious that a new crown that he had received from the royal goldsmith was not pure gold, as claimed. Archimedes was ordered to determine whether the crown was in fact made of pure gold, with the condition that only a nondestructive test would be allowed. Rather than answer the problem in the politically most expedient way (or perhaps extract a bribe from the goldsmith), Archimedes thought about the problem scientifically. The legend relates that when Archimedes stepped into his bath and caused it to Figure 1 of 1 V PartA ._ .._-. -l'. . .._ ._.. -... .._. overflow, he realized that he could answer the challenge by comparing the volume of water displaced by the crown with the volume of water displaced by an amount of pure gold equal in weight to the crown. If the crown was made of pure gold, the two volumes would be equal. If some other (less dense) metal had been substituted for some of the gold, then the crown would displace more water than the pure gold. A similar method of answering the challenge, based on the same physical principle, is to compute the ratio of the actual weight of the crown, Wactual, and the apparent v A similar method of answering the challenge, based on the same physical principle, is to compute the ratio of the actual weight of the crown, Wactual, and the apparent weight of the crown when it is submerged in water, Wappamnt. See whether you can follow in Archimedes' footsteps. The figure shows what is meant by weighing the crown while it is submerged in water. (Hem) Practice Problem 14.2 In this example we see how thermal expansion can actually throw off the accuracy of a length- measuring devicenamely, a tape measure. A surveyor uses a steel measuring tape that is exactly 50.000 111 long at a temperature of 20 C. What is its length on a hot summer day when the temperature is 35 C? I Review | Constants SOLUTION SET UP AND SOLVE We have L0 = 50.000 In, To = 20 C, and T = 35 C. We use the following equation to find AL: AL = aLo AT (Note that because AL is usually much smaller than L0 , we need to keep more significant figures in the lengths than in the temperatures.) The coefficient of linear expansion for steel is 1.2 X 105 K'1 . Using the same equation, AL = (1L0 AT = (1.2 x 10*5 K'1)(50 m)(35 C 20 C) = 9.0 x 10*3 m = 9.0 mm The new length is L 2 L0 + AL = 50.000 111 + 0.0090 m = 50.009 111 REFLECT The measuring tape lengthens by 9 mm, or 0.018%. In surveying a baseball field, this amount is negligible, but not when measuring the length of a steel bridge. Note that, although L0 is given to five significant figures, we need only two of them to compute AL. V Part A - Practice Problem: A concrete slab forming part of a driveway is 40.000 111 long when the temperature is 20 C. How much does the driveway increase in length when the temperature increases to 30 C? The coefficient of linear expansion for concrete is 1.2 X Hr5 K\". Express your answer in millimeters to two significant figures. Problem 14.36 The evaporation of sweat is an important mechanism for temperature control in some warm- blooded animals.