# Lab 12: --Buoyancy

BUOYANCY

Problem: What is the relationship between the volume of a boat and the weight it can hold?

Background: You often hear of a boat sinking because too many people have gone on board. Today you will learn how scientists and engineers can predict what the maximum number of people should be on a boat. Before you begin this project you should review some basic concepts in buoyancy, and density.

Rember from class that Density = Mass/Volume. To find the density of an object we must first find the objects mass and volume. For the rectangular boats used in today's experiment you must use the formula Volume = length x width x height. To find the mass of the boat use the triple beam balance.

Since the density of water is equal to 1 gm/cu.cm., any object that has a density more than 1 gm./cu.cm. will sink in water. As long as the density is less than 1 gm/cu.cm the object will float in water. What keeps the object floating is called the buoyant force. This is the upward force of a fluid that exists because the pressure of a fluid varies with depth. If the upward force is more than the downward force the object will float.

Background Questions.
1) What is density?
2) How do we calculate the density of a solid rectangular object?
3) What is the density of a mass block (34 g.) that has the dimensions 3cm. 6cm. x 2cm.
4) Would you expect the block to float or sink? Explain your answer.
5) What is the force that keeps objects floating called? Why does this force exist?
6) What must be done to overcome the buoyant force?

Hypothesis: Discuss with your group (and justify) a hypothesis to the question stated in the problem.

Procedure:

1) construct 5 boats using aluminum foil. Each boat should have a height of 1cm. The base of each boat should be a square with dimensions shown below.

NOTE: Try to construct the boats using the least amount of aluminum foil and NO scotch tape. Refer to you class notes. Remember a boat that is 3 x 3 x1 cm. requires a piece of aluminum foil that is 5 x 5 sq. cm. Then fold up the sides (each 1 cm.) to give the boat a height of 1 cm. Discuss this with your group.

1) 3x3x1 cm.
2) 4x4x1 cm.
3) 5x5x1 cm.
4) 6x6x1 cm.
5) 7x7x1 cm.

2) Start with the smallest boat. Fill the 1000 ml. beaker 2/3 of the way up with water. Float the boat. Start adding pennies, one at a time. Make sure not to put all the pennies in one location of the boat.

3) Count how many pennies it takes to sink the boat. Repeat this for each boat.

4) Copy the following table into your notebook.

 Boat I Boat II Boat III Boat IV Boat V number of pennies needed to sink boat Mass of boat alone (this is a very small value) Mass of boat with pennies Volume of boat density of boat without pennies density of boat with pennies

Results:
1) Include your table in the results section.
2).Collect the data and plot a graph of the number of washers needed to sink the boat (y-axis) vs. volume of boat (x-axis)
3) Include in your results section anything you observe of interest.

Discussion: Include the following questions in your discussion
1) What were the variable in this experiment?
2) What factors were held constant?
3)What is the common factor in each case for sinking the boats.
4) What is buoyancy and how does it relate to your experiment.
5) Would the shape of the boats make a difference? Explain your answer.
6) What significance is the slope of the graph you plotted?
7) Is the mass of the boat a significant factor in the boat sinking? Explain your answer.

#### What are Mathematical Relationships

What is a mathematical relationship and WHAT ARE THE DIFFERENT TYPES OF MATHEMATICAL RELATIONSHIPS that apply to the laboratory exercises in the following activities.

#### Labs

Lab 1:    The Spring Constant  -- Problem:  What is the relationship between how much a spring stretches and the force pulling on the spring?

Lab 2:    The Pendulum  --Problem: What is the relationship between the period of a pendulum and the length of the string of  the pendulum?

Lab 3:   Mass, Volume and Density--   Problem: What is the relationship between the mass of a ball and its volume assuming a constant density?

Lab 4:   Light Intensity--  Problem: What is the relationship between the intensity of a beam of light and the distance from a light source?

Lab 5:   Acceleration--  Problem: What is a the relationship between how the distance travels and the time in travel for an accelerating object?

Lab 6:   Polarization --  Problem:  What is the relationship between how much light passes through a Polaroid filter and the angle the filter is rotated?

Lab  7:   Ohms Law--  Problem:  What is the relationship between current, voltage when there is a constant resistance in an electric circuit.

Lab 8:   Radioactive Decay-- Problem: What is the relationship between the decay of radioactive material and the time allowed for the decay?

Lab 9: Water Pressure-- Problem: What is the relationship between water pressure and depth of water?

Lab 10: Attractive and Repulsive Forces--   Problem: What is the relationship between the distance between two magnets  and the force between them?

Lab 11: Damping Motion--  Problem: What is the relationship between the height a ball bounces and the number of times it has bounced?

Lab 12: Buoyancy - Problem: What is the relationship between the volume of a boat and the weight it can hold?