Exercise 2: Planning your Experiment
In Exercise 3, you will determine the density of a floating object (such as an apple). Before doing so, let’s explore Archimedes’ Principle to better understand the forces acting on the object.
As you discovered in the Warm-Up, the formula for the buoyant force acting on an object is:
[latex]F_{buoyant} = {\rho}_{fluid}gV _{submerged}[/latex]
where:
- [latex] {\rho}_{fluid}[/latex] is the density of the fluid,
- [latex]g[/latex] is the acceleration due to gravity,
- [latex]V _{submerged}[/latex] is the volume of fluid displaced by the object.
When an object is fully submerged, the displaced volume equals the entire volume of the object. However, when an object is floating, it is only partially submerged; only the submerged volume is used to calculate the buoyant force.
If you place an apple in water it floats. Use this scenario to answer the following exercises:
Exercise 2.1 (2 mark)
Draw the FBD for the forces that are acting on an apple as it floats on the water, and make sure you properly label the forces. Note that on a large body, such as an apple, surface tension is negligible and can be ignored; it should not be included on your FBD. Submit your work to Crowdmark.
Exercise 2.2 (2 mark)
Write an equation for the forces acting on the apple as it floats on the water. Since the apple is stationary, your equation should look like this:
[latex] F_{net} = [sum\,of\,all\,forces] = ma = 0\,N[/latex]
where [sum of all forces] is a list of all the forces acting on your object. Make sure you include the correct sign for your forces. Take up to be the positive direction. Be sure to write this equation in terms of known variables: volume of your object, volume displaced, density of water, and acceleration due to gravity. Hint: The mass of an object can be rewritten using its density and volume. Upload your response to Crowdmark.
Exercise 2.3 (1 mark)
Now that you’ve determined the forces at play, rearrange your equation to find an expression for the density of the apple in terms of the density of water (1000 kg/m3), the volume of the apple, and the volume of the apple that is submerged. Compare your answer to the multiple choice options below. Choose correct answer on Crowdmark.
a. [latex]{\rho}_{apple} = \frac{V _{submerged}}{1000V_{apple}}[/latex]
b. [latex]{\rho}_{apple} = \frac{1000V _{apple}}{V_{submerged}}[/latex]
c. [latex]{\rho}_{apple} = \frac{1000V _{submerged}}{V_{apple}}[/latex]
d. [latex]{\rho}_{apple} = \frac{1000gV _{submerged}}{V_{apple}}[/latex]
e. [latex]{\rho}_{apple} = \frac{V _{apple}}{1000gV_{apple}}[/latex]
Before you continue!
Before continuing, be sure you have completed Exercises 2.1-2.3 which will be graded and submitted through Crowdmark.
