Archimedes Principle

Transcription

1 Saddleback College Physics Department Purpose Archimedes Principle To calculate the average density o () an egg in salt water and () a metal object suspended rom a scale (in air and then in water) by applying Archimedes Principle then comparing these densities to their theoretical values. Theory Archimedes Principle: The buoyant orce on an object equals the weight o the luid displaced by the object and is directed vertically upward. Written mathematically, the buoyant orce is F B ρ = w = m g = gv Recall ρ = m V where w = weight o luid displaced m = mass o luid displaced g = gravity ρ = density o luid displaced V = volume o luid displaced Equipment PART I Graduated cylinder Salt Room Temperature Water 600 ml Beaker Stirrer Egg Digital Balance Hydrometer Pipette PART II Digital Balance String Metal Object (Cu, Al, Pb, Sn or Zn) Beaker Room Temperature Water Lab Jack Ring Stand Right Angle Clamp * Write directly on pages 4 & 5 then staple them to the inormal lab report. 1

2 Sketch egg Salt water Figure I Figure II Procedure Warning: DO NOT USE YOUR BOOK as you perorm Step 1 o PARTs I and II as they are discoveries which will likely tax your patience, but should result in signiicant learning. You are to work through each step 1 ( & II) below with ONLY YOUR LAB TEAM and i you are stuck more than ~5 minutes, approach your instructor or a hint/guidance. You and your lab partner(s) are obligated to discuss and explain any progress/reasoning to one another. : 1. Using Archimedes Principle and Newton s Law(s) derive an expression to calculate the average density o an egg submerged in salt water, assuming you can adjust the salinity o the water and that you can determine the speciic gravity (i.e. density) o the salt water at any particular salinity. Show this derivation in the calculations section o your lab report and you must bring your entire derivation to your proessor or approval beore beginning Part I o the experiment. HINT: It may help to answer the questions or irst. must be completed beore you begin o the experiment. 2. Fill a 600 ml beaker about ¾ ull with room temperature water. Gently place your egg in the water. 3. Gradually add a small amount o salt to the water and stir the mixture until the salt dissolves. When you have nearly achieved the situation describable by your derived equation in step #1 above, you will have to add the salt in very small increments and in the end you * Write directly on pages 4 & 5 then staple them to the inormal lab report. 2

3 will most likely need to add a bit o water to the solution using a water illed pipette to slightly decrease the salinity and achieve the desired results. 4. Once you have achieved the desired situation, remove egg and pour saltwater into a dry graduated cylinder then use the hydrometer to measure the speciic gravity o your salt water solution inside the graduated cylinder. Record this value and call it the experimental density o the salt water mixture. 5. Measure and record the mass and volume o your egg using the methods you think are most precise as these will be used to obtain an approximate theoretical density or your egg. : 1. Apply Newton s Law(s) and Archimedes Principle to determine an equation or the experimental density o the metal object, ρ o. The equation or ρ o must be only in terms o the density o the luid displaced, ρ, the mass o the object in air, m, and the mass o the object in water, m. Show this derivation in the calculations section o your lab report, including any relevant F.B.D. s. You must bring your entire derivation to your proessor or approval beore beginning o the experiment. 2. Tie string to the hook on the underneath side o the digital balance scale and suspend the metal object rom the other end o the string. 3. Set up the ring stand and place the digital balance scale on top o the ring, threading the string through the ring. 4. Measure and record the weight o the object when it hangs in air. Be sure to zero the digital balance scale while holding up the metal object. 5. Fill the beaker with enough water that the object can be submerged and place it on a lab jack, underneath the suspended mass. The bottom o the object should be almost touching the water. See picture above. 6. Slowly raise the water until the object is submerged completely. Measure and record the weight o the object when submerged in water. * Write directly on pages 4 & 5 then staple them to the inormal lab report. 3

4 Data Mass o Egg Volume o Egg Item Experimental Density o Saltwater (Hydrometer) Experimental Density o Egg Theoretical Density o Egg (mass/volume) Type o Metal (or object) Mass o Object in Air, m Mass o Object in Water, m Experimental Density o Object Theoretical Density o Object Value Analysis 1. Calculate the theoretical density o your egg by using mass per unit volume o the egg. Determine the percent dierence between the measured and theoretical density o your egg. 1. Calculate the experimental density o your object using the equation you derived. 2. Look-up the handbook value (see Appendix F in textbook) or the density o your metal cylinder and compare it to your measured density. Questions (Answer these beore you leave lab today!) Answer the three questions below in terms o orces and in terms o densities. 1. An object sinks when. 2. An object loats but is submerged when * Write directly on pages 4 & 5 then staple them to the inormal lab report. 4

5 . 3. An object loats, partially submerged when. 1. Does a ship loat higher or lower in saltwater versus in reshwater? Why? 2. A pure ice cube is in a glass o pure water and the water level is noted. When the ice cube melts, does the water level go up, down or remain unchanged? Why? 3. An ice cube that contains pure water but also has grains o sand rozen in it is placed in a glass o pure water and the water level is noted. When the ice cube melts, does the water level go up, down or remain unchanged? Why? * Write directly on pages 4 & 5 then staple them to the inormal lab report. 5