39 When researchers find a reasonably complete fossil of a dinosaur, they can de

Question

39 When researchers find a reasonably complete fossil of a dinosaur, they can determine the mass and weight of the liv- ing dinosaur with a scale model sculpted from plastic and based on the dimensions of thefossil bones. The scale of the model is 1/20; that is, lengths are 1/20 ac- Fig. 13-40 Problem 39 tual length, areas are (1/20)2 ac- tual areas, and volumes are (1/20)3 actual volumes. First, the model is suspended from one arm of a balance and weights are added to the other arm until equilibrium is reached. Then the model is fully submerged in water and enough weights are removed from the second arm to reestablish equilibrium (Fig. 13-40). For a model of a particular T. rex fossil, 637.76 had to be removed to reestablish equilibrium. What was the volume of (a) the model and (b) the actual T. rex? (c) If the density of T. rex was approximately the density of water, what was its mass?

Explanation / Answer

According to Archemedes principle, loss in the mass of the immersed model = mass of the water displaced = 637.76grm

(a) hence volume of the model = volume of the water displaced

= Mass/density. = 637.76/1. = 637.76 cc.

Hence according to the scale, volume if real T. rex

= (20)3× 637.76 cc = 8000 × 637.76

= 5102080 cc

(c) density of T. rex = density of water = 1g/cc

Hence mass of T. rex = volume × density

= 5102080 × 1 grm

= 5102.08 kg

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