(a) Calculate the buoyant force on 10,000 metric tons (1.00 x 10⁷ kg) of solid steel completely submerged in water, and compare this with the steel's weight.

(b) What is the maximum buoyant force that water could exert on this same steel if it were shaped into a boat that could displace 1.00 x 10⁵ m³ of water?

Strategy for (a)

To find the buoyant force, we must find the weight of water displaced. We can do this by using the densities of water and steel given in Table 11.1. We note that, since the steel is completely submerged, its volume and the water’s volume are the same. Once we know the volume of water, we can find its mass and weight.

Strategy for (b)
Here we are given the maximum volume of water the steel boat can displace. The buoyant force is the weight of this volume of water.

Data given in Table 11.1

Transcribed Image Text:

Substance Solids Aluminum p(x10³ kg/m³ or g/mL) 2.7 Substance Liquids Water (4°C) p(10³ kg/m³ or g/mL) 1.000 Substance Gases Air p(103 kg/m³ or g/mL) 1.29 x 10-3