Nadia Naghi. Hung Do. Minh Lu. George Manoli PHYS Lab 12: Archimede s Principle. July 2, 2014

Transcription

1 1 Nadia Naghi Hung Do Minh Lu George Manoli PHYS 2125 Lab 12: Archimede s Principle July 2, 2014

2 2 ABSTRACT: This experiment studies the principle of density by applying Archimedes principle and calculating the densities of two solids by and comparing the results to the correct values. PROCEDURE: The equipment used in the experiment was the following: triple beam balance, a metal object, graduated cylinder, and wooden cylinder. 1. Tie a string to the metal object and submerge it in a graduated cylinder filled with water. Measure its volume from the amount of water it displaces. 2. Remove the object and tie the other end of the string to the hook underneath the pan of the triple beam balance. Read the mass M of the metal object. 3. Keeping it the same, submerge the metal object in the graduated cylinder and read its apparent weight. Be sure that the object is not touching the side of the cylinder and that there are no bubbles. 4. Replace the metal object with the wooden object. With a vernier caliper, measure its radius and length. 5. As in procedure 2, read its mass M. 6. Attach a sinker to the bottom of the wooden object and submerge only the sinker in the water. Read the apparent mass. 7. Read the apparent mass while both the sinker and the wooden object are submerged in the water. DATA AND CALCULATION: Part 1: Density of metal object Mass M of metal object: kg Volume of metal object: 0.01 L Apparent mass M a of metal object: 0.060g Density of water: 1000 kg/m 3 = 1 kg/l The density of the metal object is: The density of the metal object with apparent mass is: Percentage difference between the two results is:

3 3 Part 2: Density of wooden object Mass M of wooden object: kg Radius of wooden object: m Length of wooden object: 0.1 m Apparent mass M s : 0.23 kg Apparent mass M w : 0.05 kg Volume of the wooden object is: The density of the wooden object is: The density of the wooden object with apparent mass is: The percentage difference between the results is: PRE LAB QUESTIONS: 1. State Archimedes principle. Archimedes principle states that any object totally submerged in a fluid of density f is buoyed up by a net upward force B that equal to the weight of the fluid displaced by the object. The displaced fluid is that volume of fluid equal to the volume of the object below the fluid surface such that B = f gv. 2. Use Archimedes' principle to prove the following: "When a body is floating on a liquid, it displaces a weight of liquid equal to its own weight."

4 4 In determining whether a given body will float in a given fluid, both weight and volume must be considered; that is, the relative density, or weight per unit of volume, of the body compared to the fluid determines the buoyant force. If the body is less dense than the fluid, it will float or, in the case of a balloon, it will rise. If the body is denser than the fluid, it will sink. 3. How would you determine the density of an irregularly shaped rock? Since density is defined as the mass of a unit volume of material, you would measure the volume of the rock by putting it into a container half filled with water and then measure the volume change. 4. Lead has a greater density than iron, and both are denser than water. Is the buoyant force on each one the same? Explain. Yes, the buoyancy force on both is the same. The buoyancy force is equal to the mass of the water displaced. So if a lead weight is 1 ml in volume, the buoyancy force is 1 gram (weight of the water). If an iron weight is 1 ml in volume, the buoyancy force is still 1 gram (weight of the water). If you place an object in water that is 1 ml in volume and weighs less than one gram, the buoyancy force is enough for it to float. 5. A beaker resting on a scale contains a fluid. If an object is submerged in the fluid, how would you find the increase in the reading of the scale? By the weight of the object submerged. POST-LAB QUESTIONS: 1. The bubble will not affect the density of the metal but it might well affect the measurement of the density. Finding the weight of a piece of metal in air and then finding the weight of the same piece of metal while it is suspended in water, is a quick and convenient method of finding the density of the metal. But care must be taken to avoid air bubble trapped on the surface of the metal - such bubbles will increase the amount of water displaced by the dunked metal, in turn increasing the upthrust on the metal (+ bubbles) and reducing the apparent weight in water. This will make the density of the metal appear to be lower than it actually is. When metal ( such as magnesium) react with water, bubbles of hydrogen can build up on the surface and reduce the density of the (metal + trapped bubbles) to such a level that the metal floats to the surface. Once there the bubbles usually burst and the metal sinks down again. 2. D=m/v

5 5 3. Buoyant force is equal to the weight of water displaced by the object, therefore in this situation, find the volume of the two blocks first which is 69.9 cm^3 all together. The weight of water they displaced would equal 69.9 cm^3 times 1g/cm^3 (which is the density of water) this turns out to be 69.9 g of water. from here, just subtract their combined weight with the buoyant force (225 g + 25 g g) and you will get the apparent weight, which is g. 4. Weight of block = 0.53Vg, (where g=acceleration due to gravity) Volume of immersed part of block= Vf Volume of oil displaced = Vf Weight of oil displaced = 0.8Vfg (where g=acceleration due to gravity) When an object floats, its weight equals the weight of liquid displaced, so 0.53Vg = 0.8Vfg f = 0.53/0.8 = 0.66 to 2 significant figures. CONCLUSION: After performing the experiment, we can conclude that the force present in which the fluid exerts on an object placed in it is equal to the weight of the fluid the object displaces. Archimedes principle also allows the determination of the density of an object that is so irregular in shape that its volume cannot be measured directly. If the object is weighed first in air and then in water, the difference in weights will equal the weight of the volume of the water displaced, which is the same as the volume of the object. Thus the density of the object can readily be determined. Through our experiments, we came up with a percent error of 18.2% for the metal object and 16.16% for the wooden object. This indicates that our measurements were inaccurate to some degree due to mis-readings and the object touching the sides of the cylinder sometimes.