1. Purpose
The purpose of today’s lab is to investigate Archimedes’ Principle and buoyant forces.
First, we will determine the density of metal balls of the same substance, but different radii.
Then, once this density is known, we will use a metal slug (made of the same metal) to find the buoyant force of 4 different liquids and determine the density of these liquids.

2. Activity 1: Finding the density of the metal spheres
Force sensor
Metal tray (place the metal spheres into the tray)
Glass cylinder filled with water.
Please remember to only fill water into the glass cylinders and not any other type of liquid.

3. Activity 2: Finding Fluid Densities
You will find 4 different plastic/paper cup containers filled with the following liquids:
Tap Water (get yourself)
Salt Water
Corn Syrup (paper cup)
Vegetable oil (paper cup)
Attach the cylindrical metal mass to the end of the force sensor, and place it into the substances to measure force.
Cylindrical metal mass

4. Archimedes’ Principle
An object that is submerged in a liquid will experience an additional upward force (due to the submersion) that is equal to the weight of the amount of liquid that was displaced by the object. This force is called the “buoyant force”.
Translated into simpler language, this means:
An extra force acts on an object when it is placed, for example, in water. This makes the object appear lighter than it really is.

5. Example of a buoyant force
A metal ball of volume 50cm3 fully submerged in water will experience a buoyant force of the following magnitude:
mass of displaced water
density of water
volume of ball

6. Free Body Diagram (3 forces)
string
density of water T
volume of ball
density of metal

7. Using Newton’s Second Law…
In this static situation there is no acceleration, therefore  
 By measuring T and V, and knowing the density of water and the acceleration of gravity, the density of the metal can be calculated.

8. In Activity 1, we will use metal spheres in water:
In Activity 2, we will use a cylindrical metal object in a fluid:

9. There is one more idea you will want to consider before starting Activity 1
Remember to “Tare” your force sensor in a clever way before any procedure. In this case, first hang the empty basket on the force sensor and into the water. THEN tare the force sensor. This will negate both the weight of the basket and the buoyant force on the basket in your force measurement!
Tared this way, when you graph the tension versus r3 in Excel, you should expect the line to go through the origin. Why do you think this is?

10. In Activity 1 (spheres) 
Measure T for different size spheres (different radii) and determine the density of the spheres.
measured
calculated
measured
What is the slope?
Get rm from slope.
plot

11. Careful when doing the Excel Plot of T versus r3
Plotting T versus r3 and using m3 as your unit results in a large number for the trendline slope.
When you display the trendline equation in the trendline label, not all digits of the slope may be displayed. So, your slope k result may be off by a factor of 10 or 100 etc.
Here is how to fix it:
Right click on the trendline label (not on the trendline).
Choose “Format Trendline Label”
Choose “Number” or
Choose “Scientific” with 3 or 4 digits.

12. For Activity 2 Step 3: Hang slug into Liquid. This way you
measure only Fbuoyant
Step 1: Hang slug
on force sensor
Step 2: Tare the
force sensor
Tare

13. Then get the density of the liquid from the measured buoyant force using the equation:
Note: You will need to figure out the volume of the slug somehow!.

14. Activity 3
Determine the density of the fluids again by measuring mass and volume of the fluid:
This method of determining the density will give you a direct comparison to the density results obtained from the buoyancy measurement.
Note: It will be easiest to measure an empty plastic container first.

15. Final Reminder
DO NOT POUR ANYTHING BUT WATER down the drain (not even the salt water which we reuse)!
DO NOT POUR ANYTHING BUT WATER into the tall glass cylinders!
Clean up anything that spills IMMEDIATELY! These can damage equipment in the lab! Use a paper towel or a sponge
Put the cardboard covers back on the paper cup containing the syrup before you leave.