Question

an object experiences a buoyant force of 15.9 n when immersed in a fluid of density 917 kg/m³. what is the volume of the object? ? m³

Explanation:

Step1: Recall Archimedes' principle

Archimedes' principle states that the buoyant force \( F_b \) is equal to the weight of the fluid displaced, so \( F_b=
ho V g \), where \(
ho \) is the density of the fluid, \( V \) is the volume of the displaced fluid (which equals the volume of the object when fully immersed), and \( g = 9.8\ m/s^2 \) is the acceleration due to gravity. We need to solve for \( V \), so we can rearrange the formula to \( V=\frac{F_b}{
ho g} \).

Step2: Substitute the given values

We know \( F_b = 15.9\ N \), \(
ho=917\ kg/m^3 \), and \( g = 9.8\ m/s^2 \). Plugging these into the formula:
\( V=\frac{15.9}{917\times9.8} \)

Step3: Calculate the denominator first

Calculate \( 917\times9.8 = 917\times(10 - 0.2)=9170- 183.4 = 8986.6 \)

Step4: Calculate the volume

Now divide \( 15.9 \) by \( 8986.6 \): \( V=\frac{15.9}{8986.6}\approx0.00177\ m^3 \) (rounded to three decimal places)

Answer:

\( \approx 0.00177 \)