Question

1. recall that density depends on both mass and volume. (density = m/v, where m is mass and v is volume.) ships are often built using heavy materials, such as steel. how can these ships float when their masses are increased by using such heavy materials?

Explanation:

Step1: Recall buoyancy principle

A ship floats when the buoyant force equals its weight. Buoyant force $F_b=
ho_{liquid}gV_{displaced}$, where $
ho_{liquid}$ is the density of the liquid (e.g., water), $g$ is the acceleration - due - to - gravity, and $V_{displaced}$ is the volume of liquid displaced.

Step2: Consider ship's shape

Ships are designed with a large, hollow shape. This increases their volume $V$. Even though they use heavy materials and have a large mass $m$, the large volume allows them to displace a large amount of water.

Step3: Analyze density comparison

The overall density of the ship $
ho_{ship}=\frac{m}{V}$ (where $V$ is the total volume of the ship). By increasing the volume $V$ while adding mass $m$, the ship's density can be made less than the density of water $
ho_{water}$. When $
ho_{ship}<
ho_{water}$, the ship floats according to Archimedes' principle.

Answer:

Ships can float because they are designed with a large, hollow shape that increases their volume. This allows them to displace a large amount of water, and as long as the overall density of the ship (mass/volume) is less than the density of water, they will float despite using heavy materials.