A plastic sculpture used as an underwater marker has a fixed volume of

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Fluids · Fluids

Problem

0.015\,\text{m}^{3}

. When deployed in a mountain lake at

5^{\circ}\text{C}

, the water density is

1.00\times10^{3}\,\text{kg}\,\text{m}^{-3}

. In summer the surface temperature of the lake rises to

35^{\circ}\text{C}

, reducing the water density to

9.94\times10^{2}\,\text{kg}\,\text{m}^{-3}

. Assume the sculpture remains fully submerged and that

g=9.80\,\text{m}\,\text{s}^{-2}

throughout the year. (a) Determine the magnitude of the buoyant force acting on the sculpture in early spring at

5^{\circ}\text{C}

. (b) Determine the magnitude of the buoyant force acting on the sculpture in midsummer at

35^{\circ}\text{C}

. (c) Calculate the percentage decrease in buoyant force between the two seasons. (d) Explain qualitatively how the seasonal change in buoyant force might affect the depth at which the sculpture comes to rest if its average density is only slightly greater than that of water.

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