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

Question

When researchers find a reasonably complete fossil of a dinosaur, they can determine the mass and weight of the living dinosaur with a scale model sculpted from plastic and based on the dimensions of the fossil bones.  The scale of the model is 1/20.  First the model is suspended from an arm of a balance and weights are added to the other arm until equilibrium is reached.  The the model is fully submerged in water and enough weights are removed from the second arm to reestablish equilibrium.  For a model of a dinosaur, 637.76g had to be removed to reestablish equilibrium.  What was the volume of (a) the model and (b) the actual dinosaur?  (c) If the density of the dinosaur was about that of water, what was its mass?

Explanation / Answer

(a) the mass that had to be removed = 637.76g, i.e. the weight ofthe displaced water = 637.76g. assuming the density of water to be 1g/cc we can write: the volume of the displaced water = 637.76 cc. so the volume of the model is = 637.76 cm3 (b) since we have scaled by a factor of 1/20 in every dimension thescaling for volume will be (1/20)3. so the volume of the actual dinosaur is = 637.76/(1/20)3= 5102080 cm3 (c) in this case mass of the dinosaur will be 5102080 g ˜ 5.1ton.

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