Objective
These experiments are aimed at: a) the determination of the density of an irregularly shaped object from the volume of fluid displaced when it is immersed in a fluid and it's mass when measured on a balance and b) the demonstration of the principles governing fluid behaviour.

Equipment
See the Java and Shockwave applets below.

Definition
The Shockwave applet below shows a simple experiment that tests how well various objects float in water (and other liquids). The basic idea is to grab an object, drag it to the scale, and note its mass. Then, you'll drag this same object to the graduated cylinder to figure out its volume. You'll use its mass and its volume to figure out its Density (recall that the density of a substance is its mass divided by its volume; or, in symbolic terms, D = m/V).

Finally, based on the density of the object, and the density of the fluid, you'll make a guess or hypothesis as to whether or not that object will float in the liquid. You'll then repeat this for various objects and various fluid densities.

In the other part, the Java applet shows a simple experiment concerning the buoyancy in a liquid: A solid body hanging from a spring balance is dipped into a liquid by dragging the mouse. In this case, the measured force, which is equal to the difference between the weight and the buoyant force, is reduced. This is symbolized as: F_measured = F_gravity - F_buoyant, where the weight is simply the force due to gravity (w = F_gravity = mg). Finally, the Law of Archimedes tells us that the buoyant force is equal to the weight of the replaced liquid. This is symbolized by: F_buoyant = w_{replaced_water}.

Procedure

Part A: Density

URL: http://ippex.pppl.gov/interactive/matter/denslab.html

1. For five of the 10 objects (blue square, blue triangle, red square, red oval, pink square, purple oval, green triangle, grey triangle, tan rectangle, and red/black rectangle):
   1. Use the scale to measure the mass of each object
   2. Use the graduated cylinder to measure the volume of each object
   3. Calculate the density of each object
2. Using the chart under the Help screen (click the ? to display the help screen), identify the type of each object.
3. Set the density of the liquid to 1 gm/cc
4. For each object, record your guess (hypothesis) of whether or not it will float in the pail
5. Place each object in the pail and confirm/deny your hypothesis
6. For each object, record your guess (hypothesis) of whether or not it would float if the density of the liquid was raised to 2 gm/cc
7. Change the density of the liquid to 2 gm/cc and confirm/deny your hypothesis by placing each object in the pail

The Shockwave Applet:

Part B: The Buoyant Force

URL: http://home.a-city.de/walter.fendt/phe/buoyforce.htm

1. Set the base area and height of the body to your liking
2. Set the density of the body (D_body) to < 1.0 gm/cc
3. Record the volume, density, and weight of the body
4. Lower the body into the water and record the Buoyant Force, F_B, on the body and the weight_water that was displaced
5. How does the F_B compare to w_body?
6. Does the body float?
7. Repeat the above for a D_body = 1.0 gm/cc and for a D_body > 1.0 gm/cc

The Java Applet:

You can change (within certain limits) the preselected values of base area, height and densities by using the appropriate text fields. After you have pressed the "Enter" key, the program will indicate the new values of depth, replaced volume, buoyant force, weight and measured force. A gravitational acceleration of g = 9.81 m/s2 was presupposed.

If you see the words "Maximum exceeded!" (red letters), you have to choose an adequate measuring range.

Law of Archimedes: The buoyant force is equal to the weight of the replaced liquid or gas.

Questions

1. In Part A, what is the relationship between the density of each object and whether or not it floats in the pail?
2. In Part B, is there a relationship between the volume (& density) of the body, density of the liquid, and whether or not the body floats in the liquid?
3. In Part B, how does the weight of the replaced water relate to the F_B? Can you calculate the weight of the replaced water if you know D_water = 1.0 gm/cc?

Notes

• Some program notes:
  • 1 cc = 1 ml = 1 cm³
  • draught = the depth of a vessel's keel below the surface
  • The object is the same thing as the body
  • Density is D = ^m/_V and the Weight is w = m · g
  • Some of the objects in the first part cannot be identified by their density (they are unknown)
  • Weight_{replaced water} = F_B (in part B)
  • Don't forget to press ENTER (in part B) in order to register the values you change
  • In part B, there might be a bug if you set D_body=0.5 (shows weight of replaced water as 2.45N instead of 2.35N) so avoid that setting
• Be sure to use the correct units for each measurement and calculation!
• Record all data directly in your lab notebook