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 1/25; that is, lengths are 1/25 actual length, areas are (1/25)^2 actual areas, and volumes are (1/25)^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 (the figure). For a model of a particular T. rex fossil, 687 g had to be removed to reestablish equilibrium. What was the volume of (a) the model (in cm^3) and (b) the actual T. rex (in m^3)? (c) If the density of T. rex was approximately the density of water, what was its mass?

Explanation / Answer

(a)

the weight ofthe displaced water = 687 g

the volume of the displaced water = 687 cc(density of water to be 1g/cc)

so the volume of the model is = 687 cm3

(b)

in every dimension the scaling for volume will be (1/25)3.

volume of the actual dinosaur is

= 687/(1/25)3

= 10734375 cm3

(c)

mass of the dinosaur = 10734375 g

= 10.7ton.

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