Density of Non-Geometric Objects - Online Tutor, Practice Problems & Exam Prep

To calculate the density of non-geometric objects, water displacement is used to determine their volume. When an object is submerged, it displaces a volume of water equal to its own. For example, if the initial water volume is 3.5 mL and rises to 5.8 mL after submersion, the volume of the object is calculated as 5.8 mL - 3.5 mL = 2.3 mL. This method is essential for understanding concepts like density and volume in practical applications.

Density of Non-Geometric Objects Concept and Example

Hey everyone. So when it comes to calculating the density of non-geometric objects, we have to utilize what's called water displacement. Now, water displacement is just the amount of water moved out of the way when an object is totally submerged. Here we're going to say water displacement can be used to determine the volume of non-geometric objects.

Let's look at this example. It says, calculate the volume of the water displaced by the submerging of the object. Here, the volume of the given cylinders is in milliliters. So, if we take a look here, there's nothing inside of this first tube here, and we're going to approximate what the volume is. It kind of looks like it touches around this line. So, we're going to say this is approximately 3.5 milliliters.

Now we've taken our non-geometric object and placed it within the water. This causes a rise in the water level. If we take a look here, we say that our new volume, it's a little bit harder to see. We're going to say that it's not quite 6 ml. We're going to say here that it's approximately 5.8 ml. So, we are going to say we have 5.8 ml after we've submerged the non-geometric object.

So, the volume of the object would just be our final volume of 5.8 milliliters minus our initial volume of 3.5 milliliters. So that would give me a volume of the non-geometric object of 2.3 milliliters. So, 2.3 milliliters would be my final answer for this example question.

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

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

Here’s what students ask on this topic:

How do you calculate the volume of a non-geometric object using water displacement?

To calculate the volume of a non-geometric object using water displacement, follow these steps: First, fill a graduated cylinder with a known volume of water and record this initial volume (V_initial). Next, carefully submerge the non-geometric object into the water, ensuring it is fully submerged. Record the new water level, which is the final volume (V_final). The volume of the object (V_object) is then calculated by subtracting the initial volume from the final volume: $V_{\mathrm{object}}=V_{\mathrm{final}}-V_{\mathrm{initial}}$. For example, if V_initial is 3.5 mL and V_final is 5.8 mL, then V_object is 2.3 mL.

What is the principle behind water displacement in measuring volume?

The principle behind water displacement in measuring volume is based on Archimedes' principle. This principle states that when an object is submerged in a fluid, it displaces a volume of fluid equal to the volume of the object. This method is particularly useful for non-geometric objects whose volume cannot be easily calculated using standard geometric formulas. By measuring the change in water level before and after submersion, the volume of the object can be determined accurately.

Why is water displacement an effective method for measuring the volume of irregular objects?

Water displacement is an effective method for measuring the volume of irregular objects because it relies on the physical property that an object will displace an amount of water equal to its own volume when fully submerged. This method bypasses the need for complex calculations or assumptions about the object's shape, providing a straightforward and accurate way to determine volume. It is especially useful for objects that do not have regular geometric shapes, making traditional volume calculation methods impractical.

Can water displacement be used to measure the volume of all types of materials?

Water displacement can be used to measure the volume of most solid materials, provided they do not dissolve, react with water, or float. For materials that float, a weight can be used to fully submerge the object, and the volume of the weight must be accounted for in the final calculation. For materials that dissolve or react with water, alternative fluids that do not cause such reactions can be used. However, the principle remains the same: the volume displaced by the submerged object equals the volume of the object.

How do you calculate the density of a non-geometric object after finding its volume?

To calculate the density of a non-geometric object after finding its volume, you need to know the object's mass. First, measure the mass of the object using a balance. Then, use the volume obtained from the water displacement method. The density (ρ) is calculated using the formula: $\rho =\frac{\mathrm{mass}}{\mathrm{volume}}$. For example, if the mass of the object is 4.6 grams and the volume is 2.3 mL, the density would be $4.6/2.3=2.0 g/\mathrm{mL}$.