Physics

Problem

A solid rectangular prism is gently lowered into fresh water and then released. The prism has measured edge lengths of

2.0\,\text{cm} \times 3.0\,\text{cm} \times 5.0\,\text{cm}

and a mass of

0.270\,\text{kg}

. (a) Calculate the volume of the prism. (b) Determine the average density of the prism. (c) Based on your calculation, state whether the prism floats or sinks when released in water and justify your conclusion. (d) The prism is now held completely submerged and attached to a vertical spring scale. Calculate the reading of the scale while the prism is at rest under water.

Intuitive explanation

The key is comparing the buoyant force to the weight—this determines whether the prism sinks or floats. Calculate the volume of water displaced when fully submerged, then find the buoyant force using $F_b = \rho_{\text{water}} V g$ . Compare this to the gravitational force on the prism itself; if buoyancy wins, it floats and you'll need to find how much volume stays underwater at equilibrium.

Intuitive explanation

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