Archimedes Principle Objective In this experiment you will verify that the buoyant force on an object submerged in water is equal to the weight of the water displaced by the object. Apparatus Triple-beam balance, Support, S-hook, String, Scissors, Overflow can, Catch bucket, Beakers, Metal samples, Paper towels. Background Archimedes principle says that when an object is partially or completely submerged in water it experiences a buoyant force equal to the weight of the water it displaces. You will verify this by two different methods for some metal samples. In Part I you will determine the buoyant force F B directly. If you weigh the sample in air W a and again when it is submerged in water W s then the difference in these values is the buoyant force provided by the water on the sample. F B = W a W s (1) In Part II you will use what is known as an overflow can and catch bucket. Any water displaced by the sample when lowered into the overflow can ends up in the catch bucket. Thus the weight of the 1
displaced water W w is just the difference in the weight of the catch bucket and water W CB+w and the weight of the empty catch bucket W CB. W w = W CB+w W CB (2) In Part III you will use the fact that the volume V of water displaced by the sample is equal to the volume of the sample itself. Since the density of water d w is known, the product of these values is the weight is also the weight of the displaced water. W w = V d w (3) Procedure Note: The triple-beam balance you are using measures mass, not weight. However, W m so you can use mass as your your unit of weight and obtain the same results. Part I : Buoyant Force 1. If necessary, place the balance on the support and zero it. 2. Tie a piece of string to one of the samples. Now, tie the free end to the s-hook at a length such that the sample will be suspended about 3cm off the table when the hook is hung from underneath the balance. 3. Get the weight in air of the sample and record this value on the Data Page. 4. Fill the large beaker about half full of water. Get the weight submerged by letting the sample hang suspended in the water (add more water to the beaker if necessary - the sample should be completely underwater). Do not let the sample touch the side of the beaker. 5. Calculate the buoyant force using Equation 1. 6. Repeat with each of the samples. Use a new piece of string for each sample as you will need them for the next procedure. 2
Part II : Displaced Water, Weighed 1. Remove the balance from the support and place it on the table; zero if necessary. 2. Get the weight of the empty catch bucket and record this value on the Data Page. 3. Fill the large beaker about half full of water. Place the small beaker under the spout of the overflow can and pour water into the overflow can until is above the level of the drain hole inside. The excess water in the overflow can will drain into the beaker. When no more water flows out the overflow can is as full as it can be - which is what you want. 4. Slowly lower one of the samples into the overflow can until it is completely submerged in the water. Do not let it rest on the bottom of the can and keep contact with the overflow can to a minimum. 5. When water stops dripping from the overflow can you have captured all of the water displaced by the sample. Get the weight of the catch bucket and water. 6. Calculate the weight of water displaced using Equation 2. 7. Repeat with each of the samples, starting with a dry catch bucket each time. Part III : Displaced Water, Calculated 1. If necessary, remove the string from one of the samples and dry it off. 2. The samples are cubes. Measure the length of one of the sides s and record this value on the Data Page. Calculate the volume of the cube using V = s 3 = (s s s). 3. Calculate the weight of water displaced using Equation 3 (the density of water is 1g/cm 3 ). 4. Repeat with each of the samples. 3
Data Page Part I Object Weight Weight Buoyant in Air Submerged Force (g) (g) (g) Part II Object Weight of Weight of Weight of % Difference Empty Bucket and Displaced with Buoyant Bucket Water Water Force (g) (g) (g) Part III Object Length of Volume Weight of % Difference Side Displaced with Buoyant Water Force (cm) (cm 3 ) (g) 4
Questions 1. Do you feel that Archimedes principle is supported by your data; i.e., the buoyant force equal to the weight of the displaced water? Why or why not? 2. You determined the weight of the displaced water using two different methods. Which one do you have most confidence in, and why? What do you think the largest source of error is in the method you did not choose? 3. Which weighs more? a. A bucket filled to the top with water. b. A bucket filled to the top with water with a toy boat floating in it. c. The weigh the same. Why? 5