Chapter 13, Problem 1RQ

Review Question 13.1 How would you determine the density of an irregularly shaped object?

To determine

The way of calculating the density of an irregular object.

Answer to Problem 1RQ

Solution:

Calculate the weight of the object with the help of a weighing machine. Then, divide it by the acceleration due to Earth’s gravity to find the mass of the object. Next, calculate the volume of the irregular object by sinking the object in a container with a fluid of a relatively less density. Now, check the change in the volume of the container before and after sinking the object. That change is the volume of the object. Now, divide the mass and volume of object values to find the density of the object.

Explanation of Solution

Introduction:

Mass is the measure of matter present in a body. It is a measure of inertia. It is constant for any object.

Weight is the force caused by gravitational acceleration on a mass:

$W=mg$

Here, $m$ is the mass of the object and $g$ is the gravitational acceleration of Earth.

Volume is a measure of the space enclosed by the object.

Density is calculated by dividing mass and volume:

$\rho =\frac{m}{V}$

Here $\rho ,m,\text{and}V$ is density, mass, and volume of the object, respectivley.

Explanation:

Weighing machines will calculate the force Earth exerts on the body:

$W=mg$

Rearrange the above expression:

$m=\frac{W}{g}$

So, mass can be calculated by dividing weight with the acceleration due to gravity.

Now, to calculate the volume of the object, take a container that has a reading of volume on it. Assume that the initial reading of the fluid inside the container is $V_1$. Now, after sinking the object, the final volume is $V_2$.

So, the change in volume is $V_2-V_1$.

This change is equal to the volume of the object.

Write the expression for density:

$\rho =\frac{m}{V}$

Substitute $V_2-V_1$ for V

$\rho =\frac{m}{V_2-V_1}$

This will be the value of density.

Conclusion:

Mass can be found out with the help of a weighing machine. Since the object is of an irregular shape, there is no direct formula for calculating the volume of the object by geometry. So, the best way is to calculate its volume by calculating the space that the object encloses. Then, divide both values to calculate its density.