Halliday, Resnick & Walker — Fluids: Problem Problem_80

Dinosaur wading. The dinosaur Diplodocus was enormous, with a long neck and tail and a mass that was great enough to test its leg strength (Fig. 14.36). According to conjecture, the dinosaur waded in water, perhaps up to its head, so that buoyancy could offset its weight and lighten the load on its legs. To check the conjecture, take the density of the dinosaur to be 0.90 that of water, and assume that its mass was the published estimate of \(1.85 \times 10^4 \text{ kg}\). (a) What then would be its actual weight? Find its apparent weight when it had the following fractions of its volume submerged: (b) 0.50, (c) 0.80, and (d) 0.90. When almost fully submerged, with only its head above water, its lungs would have been about 8.0 m below the water surface. (e) At that depth, what would be the difference between the (external) water pressure and the pressure of the air in the lungs? For the dinosaur to breathe in, its lung muscles would have had to expand its lungs against this pressure difference. It probably could not do so against a pressure difference of more than 8 kPa. (f) Did the dinosaur wade as conjectured?