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When an object is submerged in a fluid, like water, it experiences an upward force called the buoyant force. This force is the reason why things feel lighter underwater. The buoyant force is equal to the weight of the fluid that the object displaces. In simple terms, if you drop an object in water, it will push away some of the water, and that displacement creates a force that pushes the object upwards. To determine the buoyant force in the problem, we calculated the difference between the mass of the spring in air and its mass in water. The equation was: \( F_b = m_{air} - m_{water} = 1.26 \, \text{g} - 1.11 \, \text{g} = 0.15 \, \text{g} \).This tells us that the spring displaces 0.15 grams of water when submerged, and thus experiences a buoyant force of 0.15 grams. Remember:

• The buoyant force helps us find the volume of the object when we know the density of the fluid it is submerged in.
• It's a key principle in fluid mechanics, established by Archimedes.

Density is a measure of how much mass is contained in a given volume. It tells us how tightly packed the molecules within a substance are. We calculate density using the formula:\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]In our problem, the mass of the spring is 1.26 grams, and its volume can be found using the buoyant force calculated earlier, which was 0.15 mL. Converting this force directly gives us the spring's volume because 1 gram of water equals 1 milliliter. Thus, the density of the spring is:\[ \text{Density} = \frac{1.26 \, \text{g}}{0.15 \, \text{mL}} = 8.4 \, \text{g/mL} \]This crucial calculation helps in identifying the material nature of the spring.

• If density is a high value, the material is likely dense and heavy for its size, like metals.
• In this context, we compared the calculated density with known specific gravities to determine the spring's composition.

Mass and volume are fundamental properties of matter. Mass refers to the amount of substance within an object and is typically measured in grams or kilograms. Volume, on the other hand, is the space an object occupies, measured in units like milliliters or cubic centimeters. These two properties are critical in finding out additional characteristics of materials, such as density.In the exercise, the mass of the spring was straightforwardly given: 1.26 grams when measured in air. The volume, even though not directly given, was found through the buoyant force we calculated. Since 1 gram of water equals 1 milliliter, we directly used the mass difference in air and water to determine the spring's volume as:\( 0.15 \, \text{mL} \).This combination of mass and volume allowed us to calculate the density, giving clues about the spring's material. Always remember:

• Mass is a constant for a given object, while volume can change depending on conditions like temperature and pressure.
• The relation between mass and volume underlines the concept of density.