A puffer fish has a mass of 8kg and an initial volume of v = .007m^3, Most puffe

Question

A puffer fish has a mass of 8kg and an initial volume of v = .007m^3, Most puffer fish puff up by swallowing a tremendous amount of water, but this guy has found a nifty way to store compressed air behind his gills. This means that he can transform himself into a terrorizing puff ball without changing his mass. In this particular instance he puffs up from his initial volume to a new volume of v = .012m^3, what is the net upward force that the water exerts on him, both before and after he expands his volume? In each case, he will tend to float to the surface or sink the bottom of the ocean?

Explanation / Answer

Hey!
The original density of the fish is =m/v = 8/0.007 kg/m3

   = 1142.85 kg/m3.

The density of water is 1 Kg/m3.As the density of fish is larger than that of the water , the fish will initially tend to sink.

After puffing air , the volume of the fish has changed to 0.012 m3. The new density of the fish is:

= 8/0.012 Kg/m3 =666.67 Kg/m3.

The new density of the fish is smaller than that of the water. So the fish tends to float.

The net upward force exerted by the water on the fish is :

F = mg-w.g.v   

F = 49 N upwards.

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