Purpose In this lab, we will prove Archimedes’ Principle by finding the density of a Metal Cylinder, a cork, and an unknown fluid by using Archimedes’ Principle. We will also use the PASCO Pascal’s Principle Lab Setup to investigate the use of fluid pressure as a hydraulic system to do work and we will find its mechanical advantage. Procedure For the first part of the lab we will be verifying case 3 as explained by professor. We will measure the mass of the metal cylinder using the digital balance. After measuring the mass we also gather the diameter and height using the vernier caliper to calculate its volume.
Using the mass and volume, we calculated its density. Now a beaker was filled with water and the mass was measured. The cylinder we originally used will now be suspended in the beaker full of water and the change of mass will be recorded. The difference between these gives the Buoyant Mass of the cylinder. Using formulas provided the actual density of object was calculated as well as the apparent mass in water. Next we verified the situation in case 1. The big and small diameters of the cork were measured and then the density was calculated.
Same process again, the cork will be suspended in the beaker that was full of water and we measured of how of it went in the water. The percent error was calculated between the experimental and the actual densities. Next we found the density off an alcohol solution two different ways and compared them. First we found the mass of the graduated cylinder and then we placed about 30ml of alcohol inside. The mass was measured again and the two masses were subtracted to obtain the mass of the alcohol alone. The mass of the alcohol and the volume were divided to find its density.
The cylinder was now suspended on the alcohol and the change in mass was recorded. Now the density of alcohol was calculated using the recorded data. For part 2 we had the most trouble using the Explorer GLX. We placed the unattached ends of the tubing and in the bottom of a beaker or similar container of water. The valve was kept open with the handle in line with the tubing. The small syringe was pulled out to the limit of the measuring graduation marks. It was pushed all the way in and this step was repeated several times watching the movement of the fluid and air bubbles.
Make sure the ends of the tubing do not come out of the water. As we finished the bleeding process using the 3 cc syringe we pushed the platform all the way down and pulled the piston of the syringe out to the largest volume graduation mark. We then made a stack of some weight and converted to Newtons and that equaled force out. These weights were placed in platform of the large piston. The inner diameter of the syringe was measured and the large piston and from these the area was calculated and the theoretical ideal mechanical advantages. Data.
Part 1. Finding the density of a substance using Archimedes’ Principle Density of Cylinder (MActObj)= 57. 2 grams Diameter of cylinder= 1. 268 cmLength of cylinder= 5. 118cm Volume (? *L*D2)/4)= 6. 464 cm3dactual= 8. 851 (g/cm3) (3. 1415)(5. 118)(1. 26802)/4=6. 464 cm3 Mbeaker + Water= 266. 4 gramsMbeaker + water + suspended cylinder= 272. 8 grams MB= 6. 4 grams Dexp= 8. 937 (g/cm3) 57. 2/6. 4= 8. 937 (g/cm3)MAppObj= 50. 8 grams 57. 2-6. 4= 50. 8 grams %Error1= . 971 % |8. 851-8. 937|/(8. 851)= . 971 % Density of Cork Mass of Cork= 8. 1 grams.
DBig= 4. 3 cmDSmall= 3. 6 cm DAvg= 3. 95 cmL= 3. 668 cm V (? *L*DAvg2/4)= 44. 9483 (cm3) =? (3. 668)(3. 952)/4= 44. 9483 cm3 dactual= . 180207 (g/cm3) = 8. 1/44. 9483 =. 180207 cm3 h’= . 545 cmhtotal= 3. 71cm V’= . 185079 cm3V’= ((4. 3-. 545*4. 3+. 545*3. 6)(? *3. 668*. 545))/((8*3. 71^2))= . 185079 cm3 Dexp= Dwater*V’/Vtotal=. 185079 (g/cm3) Error2= 2. 7% (1)(. 185079)/1=. 185079 |. 180207-. 185079|/. 185079= 2. 7% Density of Alcohol Volume of Alcohol= 30. 0 ml Mgraduated cylinder= 76. 7 gramsMgraduated Cylinder + alcohol= 99. 9 grams Malcohol= 22.
3 grams Dactual= . 773 (g/cm3) Mbeaker + alcohol= 198. 0 gramsMbeaker +alcohol + suspended cylinder= 203. 1 grams MB= 5. 1 grams dexp= . 789 (g/cm3) = (5. 1*8. 851)/(57. 2)= . 789 (g/cm3) % Error3= 2. 06 %MappObj= 52. 1 grams |. 773-. 789|/. 773= 2. 06 % 57. 2-5. 1=52. 1grams Part 2. Calculating Efficiency of different syringe diameters using Pascal’s Principle Diameter of Large Piston D= . 026 meters Area of Large piston=Aout= 5. 309×10-4m2 Syringe VolumeDiameter (m)Area of SyringeIMAtheo 20cc0. 0210* 3. 46×10-4* 1. 534 12cc0. 01521. 814 x 10-42.
9259 6cc0. 01281. 2868 x 10-44. 1257 3cc0. 00844 5. 5947 x 10-59. 48938 ?(. 02102)/4= 3. 46×10-4 Aout/Ain=(5. 309×10-4/3. 46×10-4)= 1. 534 SyringeForceinDistanceinForceoutDistanceoutAMAIMAWorkinWorkoutEfficiency 3cc 3. 050. 04810. 612450. 00370. 49451. 91* . 1464* . 0392* 26. 81% 6cc7. 010. 046910. 6124560. 00670. 773. 690. 3287. 071121. 63% 12cc13. 770. 061710. 6124560. 01671. 51397. 84960. 17720. 83% 20cc21. 460. 062510. 6124560. 0327. 49451. 9111. 3410. 34725. 87% Win=Fin*Din= (3. 05)(. 048)= . 1464 Wout=Fout*Dout= ( 10. 61245)(0. 0037)= .
0392 Eff= Wout/Win= (. 0392/. 1464) x 100%= 26. 81 % Extra Credit Cork MB= Density of water*V’ = Density of water*(Density of object/Density of water)(V0) = Density of Object* V0 MBtheoretical= (. 180207)(44. 9483)= 8. 1 grams Mexp= 8. 5 grams %Error= |8. 5-8. 1|/8. 5×100%= 4. 9 % Cylinder Mtheo = Density of water*Vcylnder =(1 g/cm3)(6. 463cm3) Mtheo= 6. 463 grams Mexp= 7. 6 grams %Error= |6. 462-7. 6|/7. 6×100%= 14. 97% Discussion In this lab we proved that a fluid is buoyed up by a force equal to the weight of the fluid that it displaces.
Through out the experiment we noticed that our values were not far apart from what we were supposed to obtain thus proving Archimedes Principle. There was an error of . 971 %, 2. 7% and 2. 06 % respectively for part one of this lab. It was determined that some error occurred during the procedure of the lab. This error could be a result due to the improper use of the vernier caliper and the chance that the digital balance was not correctly zeroed at the start of the experiment. These errors would cause inaccurate values of the measured weight and a false value for the volume of the cylinder, cork and alcohol.
Having these errors would be enough to offset the correct results, to a point where the experimental data is incorrect. Part two of the lab consisted in testing Pascal’s Principle. We used some type of hydraulic jack for this part. We know that according to Pascal’s Principle, a multiplication of force can be achieved by the application of fluid pressure. This allowing the lifting a heavy load with a small force as in an auto hydraulic lift, but of course there can be no multiplication of work, so in an ideal case with no frictional loss, Win=Wout. This is exactly what we did for this portion of the lab.
Using syringes of 3cc, 6cc, 12cc and 20cc we applied a force calculated using the Explorer GLX as thus proved that the thinner syringe improved the AMA and the IMA. We noticed that indeed there were some patterns in the efficiencies but we found it quite weird that the thinner syringe gave us a higher efficiency. We tried this part of the experiment more than once since at first the explorer GLX was giving us values that we did not understand thus reading a little more on Pascal’s Principle made us realize how to make sense of the results we were obtaining.
We learned that any externally applied pressure is transmitted to all parts of the enclosed fluid, making possible a large multiplication of force. For extra credit portion we were notified that we might find a high percentage of error. At first we believed that this error could be due to the cohesive force of water. As we conducted this experiment for the Cork and the Cylinder we found that the percent error wasn’t as high as we initially thought. We found that the mass of the water spilled for the Cork should equal to density of the object times its volume.
Now for the cylinder we had to find a different relationship in which we thought that the theoretical mass spilled should equal to the Density of the water times the volume of the cylinder and indeed that gave us something close to what we obtained experimentally. Conclusion As stated before, the purpose of the lab was to prove that the buoyant force acting on the metal cylinder and Cork is equivalent to the liquid displaced. This was made possible by using Archimedes’ Principle. Though the metal cylinder and Cork were tested in two different fluids, water and alcohol, the principle was proven correct.
Some errors could have been avoided if we used an electronic balance that wouldn’t give us a big uncertainty while measuring the mass of the materials used. The difference between the actual and apparent weight was small showing the accuracy of Archimedes’ Principle. Now while testing Pascal’s Principle we had a lot of trouble understanding the results. We left lab confused on the results we obtained and we even believed that we had to do the experiment all over again until I did more research on the matter.
Realizing that Pascal’s aw says that when the pressure at an point in a static fluid in a closed system is changed, the change will disperse equally throughout the fluid. That is, the pressure at a point far away from the region will change by the same amount as a point nearby. Calculating the output force in the experiment meant that we had to divide the area of the output by the area of the input then multiplying the result by the input force. And that was something we were doing wrong. We were multiplying everything wrong.
We had to realize for example that if the output has ten times the area of the input, the output force would be ten times the input force. This does not mean that extra energy is appearing out of nowhere. The amount by which the output is raised will be less than the amount by which the output is pressed down, which evens things out. By doing more thinking we realized that the experiment did not have to be repeated after all. Some equipment could have caused some of our calculated values to present some type of error but we were sure that those errors were minimal.
The syringe caused problems at the beginning since we tried our best to apply a constant force for each one the syringes. Another device was the Explorer GLX, which we were forced to replace once due to the values of force it was giving us since we believed they were wrong because the force given was constant. Finally the load we applied could have been another problem we did not look into more closely. Other than those inconveniences, we believe we have proven and understood Pascal’s Principle once after all!!!