Please fill out the rest of the tables #3-5 for the calculations, USE the measurements given to solve for them. Answer Questions #1-12. Show work for all calculations step by step and use a clear explanation.

Name(s): Date: Objective: The purpose of this exercise is to measure the buoyant force on several submerged hanging and floating objects. You will verify Archimedcs' principle by calculating the density and volume of the objects. Parts and Equipment Required: . Topic-beam balance - Vernier caliper - Graduated cylinder or beaker - Box ofassoned masses. - String - Water Introduction: Amhimedes' principle states that the displaced volume of uid exerts a buoyant force [R] on an object that is equal to the weight of the displaced uid (W1). In this experiment, a hanging object is suspended from a scale by a string. The true weight (W.} of the object due to gravity alone is measured before it is submerged. The apparent weight (W3) is measured when the object is completely submerged in a graduated cylinder or beaker that has been lled with approximately 256 mL of water. The buoyant force is then calculated from the difference between the true weight and the apparent weight, as follows: (1) Flt: WI _ we: wd An object that is. lighter than water will float. In this scenario, the buoyant force will equal the true weight of the object which is also equal to the weight of the displaced uid according to Archimedes' principle. This is expressed as follows: {2) RF W.= Wu An alternate way of calculating the bouyant force Fa. is by multiplying the density of water (1). =ltltlt} kgfms) with the displacement volume V; and the acceleration due to gravity g. in Fla" Pu Va 3 Additionally. an alternate version of the standard density formula. p..,= Mass-W a... is with the true weight W. proportional to the volume of the measured object V.\" and actual density of the object 13.\" as follows: (4) wr' Perv it]: ' WWW-bl llV owl ' B ' M355 ' B Data TABLE #1- Enter the experimentally measured force data from in the table below. (For object completely submerged in water.) Material W (N) W (N FR (N True weight Apparent weight Buoyant force #1 Copper 56.29 g 50.51 g 5. 78 g #2 Iron 63.17 g 40.05 g 23.12 g (For object floating in water.) Material W. (M) F: (N) True weight Buoyant force #1 Wood 9.56 g 9.56 g #2 Cork 9.425 g 9.425 g TABLE #2- Record the caliper measured dimensions of each object in the table below. (For objects completely submerged in water.) Material Height (cm) Diameter or Length (cm) Width (cm) Other (cm) #1 5 cm 1.33 cm Copper #2 Iron 4.56 cm 2.52 cm For objects floating in water. Material Height (cm) Diameter or Length (cm) Width (cm) Other (cm) Small End of Cork #1 Wood 1.58 cm 3.62 cm 3.63 cm #2 Cork 3.70 cm 4.49 cm 3.5 cmTABLE #3- Record the beaker or graduated cylinder measured volumes in the table below. (1 cm ' = / ml) (For objects completely submerged in water.) Material Initial volume (cm 3) Vi Final volume (cm 3) Vr Volume displaced (m') (V. = V,-V.) #1 Copper 250 cm^3 6.08 cm #2 Iron 250 cm^3 6.39 cm For objects floating in water.) Material Initial volume (cm ') Vi Final volume (cm ') Vr Volume displaced (m') (Va = Vr-V.) #1 Wood 250 cm^3 6.20 cm #2 Cork 250 cm^3 6.15 cm TABLE #4-Use the experimentally measured buoyant force (F,,) for the submerged object, or the experimentally measured weight (W.) for the floating object (since F,,= W, for floating objects) from Table #1 and equation # 3 to calculate an experimental value of the displaced volume (Va ) for each object given the density of water. Show your mathematical work. (For objects completely submerged in water.) Material Volume (m') #1 Copper #2 Iron For objects floating in water.) Material Volume (m') #1 Wood #2 CorkTABLE #5-Use the caliper measured dimensions from Table #2 and the appropriate geometric formulas for a block, sphere, cylinder, etc. to directly calculate their volume (V.). Show your mathematical work. (For objects completely submerged in water.) Material Volume (m') #1 Copper #2 Iron (For objects floating in water.) Material Volume (m') #1 Wood #2 CorkCalculations & questions 1. Determine the percent differences between the caliper measured volume (Table #5) of each object and the value calculated from the buoyant force measurement (Table #4-Archimedes' principle). Show your work. 2. Derive a formula from equations 1, 3, and 4 to calculate the density pr=Pobj of each submerged object WITHOUT the use of any volume data. (Use the data from Table #1 and the density of water ONLY) 3. Use the caliper measured volume (V.= Vej ) from Table #5 and equation 4 to calculate the density (p.=P.j) of each submerged object. 4. Use the measured weight (W.) and the beaker measured displacement volume (V.= V..j) from table 3 and equation 4 to calculate the density (pa=P.) of each submerged object. 5. Look up the density online for both submerged objects and compare your measured and calculated values of the density to the values listed. What is your guess regarding the composition of each material? 6. Which density calculation for the submerged objects is the most accurate pa ,p., or p,? Calculate the percent error as compared to the online values for each density calculation. 7. Now, derive a formula from equations 2, 3, and 4 to calculate the density of each floating object. One density (p= p.bj) should be from using the beaker measured displaced volume (V.) in table 3 from which we calculate the bouyant force (equation 3) and the other density (Pr=pobj) should be calculated from the measured weight (W.). (Hint: Both calculations of density will need the caliper measured volumes (V.= Vaj). Also, remember F.= W, for a floating object) 8. Look up the density online for both floating objects, then compare your measured and calculated values of the density to the values listed. What is your guess regarding the composition of each material? 9. Which density calculation for the floating objects is the most accurate pa or p.? Calculate the percent error for each as compared to the online (true) values. 10. What happens to the apparent weight as the objects are submerged? 11. What happens to the buoyancy force as the objects are submerged? 12. What are some of the sources of error in the experiment?L +1 H L H+h h 1 R Frustum of cone (of volume V) C Cono VE nh R' - r) OR V= nh 3 3 3 - (R' + Rr + 12) Note: Here IT is a constant whose value is 22/7 (or) 3.141592653