PHYS 1405 –Conceptual Physics I
Archimedes Principle
Leader: ______Recorder: ______
Skeptic: ______Encourager: ______
Materials
600 ml beaker
Triple beam balance
Density cylinders set
100 ml graduated cylinder
Modeling clay
Support structure for triple beam balance for weighing hanging objects
Introduction
The story is told that the Greek mathematician Archimedes liked to lounge around in his bath all day. He would work out his geometric proofs on his stomach (he was quite fat) writing with bath oil. One day when he was contemplating why things floated, the idea, which has become known as Archimedes' Principle, occurred to him. He became so excited by his discovery that he jumped out of his bath and ran through the streets of his town shouting "Eureka" which is Greek for "I've found it". In this lab we will attempt to grasp some of Archimedes' excitement by rediscovering his principle.
Part 1 Discovery Activity
Procedure
1. Roll some modeling clay into a solid ball such that it has an approximate diameter of 3 cm. Estimate the volume of the clay by treating it as a sphere. (V = R3). Determine the radius of the ball in cm so that the volume you calculate will be in cm3.
Calculated estimate of Volume of clay ball: ______cm3.
2. Fill the beaker about half-full of water. Carefully note the level of the water ______mL. Place the clay into the water and carefully note the new water level ______mL. Subtract these two to determine the approximate volume of the clay ball.
Water displacement estimate of Volume of clay ball: ______cm3 = mL.
3. Compare your estimate of the volume of the clay ball with the change of the volume of the water? Do they seem comparable? (Note that 1 ml = 1 cm3)
A liquid will tend to be as dense as it can at a given temperature, and if you apply a force to it, you cannot make it any denser. This property of liquids is known as incompressibility. Thus when you drop a solid object into a liquid, it will merely add its volume to the volume of the liquid. We describe this by saying the solid displaces its volume.
4. Now shape the clay into a thin-walled teacup shaped “boat” that can float. Make sure that there are no holes and that the sides don't flop over. Before placing the boat into the water, predict whether the water level will be higher for the boat or for the clay ball. ______Explain your reasoning.
Carefully note the level of the water ______mL. Place the boat into the water (it must float!) and carefully note the new water level ______mL. Subtract these two to determine the approximate volume of water displaced by the boat.
Water displacement estimate for clay boat: ______cm3 = mL.
5.Explain why the floating boat is receiving a larger buoyant force by discussing its change of motion when a) sinking and b) floating.
6. Explain why the floating boat is receiving a larger buoyant force by discussing the amount of water it displaces compared to when it was ball.
7. The buoyant force is equal to the ______of the displaced liquid. This is a statement of Archimedes' Principle which we will explore more quantitatively below
Part 2 Procedure for Determining Archimedes’ Principle
Safety : No eating or drinking in the lab while performing this procedure.Fill a graduated cylinder half full and record the reading. Hang one piece of the provided metal set from underneath the pan of the triple beam balance and measure the mass. To get reliable data, it is important that the mass hangs directly under the center of the pan of the balance during this procedure. Record the mass in the column labeled Scale reading (Air) in the table below. To convert from g to kg move the decimal 3 places to the left. Lower the mass so that it submerges completely in the graduated cylinder. Use the triple beam balance to determine the reading when the mass is submerged and record the value in the data table below in the column labeled Scale Reading (Water). Record the change in volume of the water in the cylinder when the mass is submerged in the column headed Displaced Volume. Determine the mass of the displaced water by multiplying the displaced volume in ml by the density of water in units of .001 kg/ml. Repeat the entire procedure for each of the different metals in the provided set so that you have a total of 5 sets of data.
Wash your hands thoroughly after completing the procedure to remove any lead dust that may have gotten on you.
Data
Weigh your objects in air and in water and record your data below. You may if you wish do the displaced water volume as a separate step from the wet and dry weighings.
Note again that 1 mL of water has mass of 1 g.
Mass Reading (in Air)(g) / Mass Reading (in Water)
(g) / Water level before submersion / Water level
after submersion / Displaced Volume
(ml) / Mass displaced water
(g)
Data Analysis and Questions
1) When the mass is suspended in air by a string, how does the weight of the mass compare to the tension in the string? Explain your answer.
2) When the mass is submerged in the liquid an extra upwards force called the buoyant force acts on it. What effect will the buoyant force have on the tension in the string? ______Explain. (note that scale readings in kg are proportional to tension forces)
3) The mass of the displaced water plus the scale reading in water should equal the scale reading in air. Is this true for your data to within about + or – 10%? ______Calculate this comparison for your best and worst case below.
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