Question

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 he published estimate of 1.85×104 kg. (a) What then would re its actual weight? Find its apparent weight when it had the ollowing fractions of its volume submerged: (b) 0.50, (c) 0.80, and (d) 0.90. When almost fully submerged, with only its head ibove water, its lungs would have been about 8.0 m below the water surface. (e) At that depth, what would be the difference setween 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 differ?nce. It probably could not do so against a pressure difference of more than 8kPa. (f) Did the dinosaur wade as conjectured?

Answer 1

To determine the actual weight and apparent weight of the dinosaur Diplodocus, we can use the given information about its density and mass. By comparing the actual weight to the apparent weight at different fractions of volume submerged, we can evaluate the conjecture about the dinosaur wading in water.

Step-by-step explanation:

To test the conjecture that the dinosaur Diplodocus waded in the water to lighten the load on its legs, we need to determine its actual weight and its apparent weight at different fractions of its volume submerged. The density of the dinosaur is given as 0.90 times the density of water, and its mass is 1.85x10^4 kg. To find the actual weight, we multiply the mass by the acceleration due to gravity. The apparent weight can be calculated by multiplying the density of water by the volume submerged and the acceleration due to gravity. Using this information, we can determine whether the dinosaur waded in water as conjectured.