Density of Non-Geometric Objects: Videos & Practice Problems

To determine the volume of irregularly shaped objects, water displacement is a practical technique. By submerging the object in water and measuring the change in water level, one can calculate the object's volume. For instance, if water in a graduated cylinder starts at 3.5 mL and rises to 5.8 mL after submersion, the object's volume is the difference:

$5.8\mathrm{mL}-3.5\mathrm{mL}=2.3\mathrm{mL}$

resulting in a volume of 2.3 mL. This method is particularly useful for objects that do not conform to standard geometric shapes, allowing for accurate volume measurements which are essential in calculating density.

Density via Water Displacement

To calculate the density of non-geometric objects, the method of water displacement is employed. This technique involves measuring the volume of water that is displaced when an object is fully submerged in water. The principle behind this method is that the volume of water displaced is equal to the volume of the object submerged.

For instance, consider a scenario where we have a graduated cylinder filled with water. Initially, the water level is at approximately 3.5 milliliters (mL). When a non-geometric object is submerged, the water level rises. After submerging the object, the new water level reads approximately 5.8 mL. To find the volume of the object, we subtract the initial water volume from the final water volume:

Volume of the object = Final volume - Initial volume

Volume of the object = 5.8 mL - 3.5 mL = 2.3 mL

Thus, the volume of the non-geometric object is 2.3 milliliters. This method is particularly useful for objects that do not have a regular shape, allowing for accurate volume measurement through the displacement of water.

A piece of unknown solid weighs approximately 0.045 lbs. When a scientist places it in a glass beaker the water level increases from 200 mL to 260 mL. What is the density of the unknown solid in g/mL?

• A. 0.5 g/mL
• B. 0..2 g/mL
• C. 0.0007 g/mL
• D. 2.9 g/mL
• E. 0.3 g/mL

Answer: (E)

If an irregularly shaped apple possesses a density of 0.96 g/cm³, what is its mass in milligrams? (The volume of the given cylinders are in mL).

• A. 4000 mg
• B. 5000 mg
• C. 0.0048 mg
• D. 4800 mg
• E. 5300 mg

Answer: (D)

Here’s what students ask on this topic:

What is the water displacement method?

The water displacement method is a technique used to determine the volume of an irregularly shaped object. This method is based on the principle of Archimedes, which states that an object submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.

Here's how it works in practice: You fill a graduated cylinder or overflow can with water to a certain level and record the volume. Next, you carefully submerge the object whose volume you want to measure into the water. As the object goes in, it pushes the water out of the way, causing the water level to rise. You then measure the new water level. The difference in volume before and after the object was submerged is equal to the volume of the object itself.

This method is particularly useful for solid objects that do not dissolve in water and have complex shapes that make it difficult to calculate volume using geometric formulas.

How can volume be found using water displacement?

To find the volume of an irregularly shaped object using water displacement, you'll need a graduated cylinder or a beaker with a known volume of water. Here's what you do:

1. Fill the graduated cylinder or beaker with a certain amount of water and record the volume (V1).
2. Gently submerge the object whose volume you want to measure into the water. Be careful to avoid splashing so that the water level rises only due to the object being submerged.
3. Record the new water level (V2).
4. The volume of the object (Vobject) is equal to the difference between the final water level and the initial water level: Vobject = V2 - V1.

This method works based on the principle of displacement discovered by Archimedes, which states that the volume of the fluid displaced is equal to the volume of the object submerged. Remember that the object must be completely submerged for this to be accurate, and it should not dissolve or react with the water.

How can density be found with water displacement?

Density can be found using water displacement by following the principle that the volume of water displaced by an object submerged in water is equal to the volume of that object. Here's a step-by-step guide:

1. Fill a graduated cylinder or overflow can with water to a certain level and record the initial volume ($V$_initial).
2. Carefully submerge the object whose density you want to find into the water without spilling any. Ensure the object is completely submerged.
3. Record the new volume of water with the object submerged ($V$_final).
4. Calculate the volume of the object ($V$_object) by subtracting the initial volume from the final volume ($V$_object = V_final - V_initial).
5. Determine the mass of the object using a balance scale before submerging it in water.
6. Finally, calculate the density ($D$) of the object using the formula:

$D=\frac{\mathrm{Mass\; of\; the\; object\; (m)}}{\mathrm{Volume\; of\; the\; object\; (V_object)}}$

Remember, density is mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). This method is particularly useful for irregularly shaped objects that would be difficult to measure using geometric formulas.