Question

Some fish have a density slightly less than that of water and must exert a force (swim) to stay submerged. What force (in N) must a 59.0 kg grouper exert to stay submerged in salt water if its body density is 1017 kg/m3?

Answer 1

Fish's weight = mg

= 59 x 9.8 = 578.2 N

Fish's volume = mass/density = 59/1017 = 0.058013765 m³

Density of sea-water = 1025kg/m³

When the fish is submerged, it displaces a volume of sea water equal to its own volume, i.e.0.058014 m³.

Mass of displaced sea water = volume x density = 0.058014 x 1025 (kg)

Weight of displaced sea water = mg = 0.058014 x 1025 x 9.8 = 582.75 N

The upthrust equals the weight of sea water displaced, so upthrust = 582.75 N.

Taking up as positive, the combined force on the fish is upthrust - weight

= 582.75 – 578.2.95 = 4.55 N

This is positive (upwards) so the fish must exert a 4.55N downwards force to counteract this and stay submerged.

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