Answer Questions #1-12. Show work for all calculations step by step and use a clear explanation. Use the measurements given in tables #1-5 to solve answer the questions.

2. Derive a formula from equations 1, 3, and 4 to calculate the density pr=pm of each submerged object W the use of any volume data. (Use the data from Table #1 and the density of water QNLI) 3. Use the caliper measured volume (Vc= Vohj ) from Table #5 and equation 4 to calculate the density (p.=p.,bj) of each submerged object. 4. Use the measured weight (W0 and the beaker measured displacement volume (V.= V0,\") from table 3 and equation 4 to calculate the density (p.=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 ,1)" or [1,? 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 floatlng object. One density {PF pm) 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 (p.=pm) should be calculated from the measured weight (Wu). (Hint: Both calculations of density will need the caliper measured volumes (V= Vm). Also, remember Fb= WI for a oating object) 8. Look up the density online for both oating 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 oating objects is the most accurate pa or p1? 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? Procedure: For object completely submerged in water (equation 1) Step 1: Zero the triple beam balance and then hang and measure and record the mass of your material selected in air to determine it's true weight (W.). Fill the graduated cylinder or beaker with 250 ml water and then completely submerge the mass. Now, measure and record the apparent weight (W.) of the mass. The object should not touch the sides or bottom of the container. Step 2: Measure and record the initial and final volumes of the water before and after the object is submerged, respectively. Step 3: Measure the approximate dimensions needed to calculate the volume of the object with the vernier caliper and record this information. (e.g, a cylinder's volume can be calculated using V=- d h or a block is just length x width x height) Step 4: Repeat this procedure for the other object chosen. Enter your force (N), caliper (m), and water level (m ') data in into the tables below. Calculations: Use the buoyant force equations 1, 3 and 4 along with the density of water (pw =1000 kg/m') to calculate the volume of both objects. Be sure to show your work. Alternatively, use the data that you measured with the beaker for the displaced volume ( Va) to calculate the volume of both objects. Lastly, use the data that you measured with the caliper to calculate the volume of both objects. Use all three of these volumes of each object and its true weight to calculate the density three different ways (Pormula, Padisplaced , Pcaliper) for each submerged object. Find some values for the density of common object's online and compare these with your calculated values to find percent error. For object completely floating in water (equation 2) Step 1: Zero the triple beam balance and then hang and measure and record the mass of your material selected in air to determine it's true weight (W,). Fill the graduated cylinder or beaker with 250 ml water and then let the mass float. Step 2: Measure and record the initial and final volumes of the water before and after the object is floating, respectively. Step 3: Measure the approximate dimensions needed to calculate the volume of the object with the vernier caliper and record this information. Step 4: Repeat this procedure for the other object chosen. Enter your force (N), caliper (m), and water level (m' ) data in into the tables below. Calculations: Use equations 2, 3, 4, and the data that you measured with the caliper, beaker, triple-beam balance along with the density of water (pw =1000 kg/m') to calculate the density of both objects. Use the caliper measured volume ( V.) of each object and its true weight (W.) to calculate the density (P, = P.bj ). Next, use the caliper measured volume (V.) of each object and the bouyant force (F.) calculated from the displaced volume (Va) to calculate the density (pa= Pobj ). Find some values for the density of common object's online and compare these with your calculated values to find the percent error. 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) FB (N) True weight Apparent weight Buoyant force #1 Copper 56.29 g 50.51 g 5.78 N #2 Iron 63.17 g 40.05 g 23.12 N For object floating in water. Material W, (N) FB (N) True weight Buoyant force #1 Wood 9.56 g 9.56 N #2 Cork 9.425 g 9.425 NTABLE #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) Copper #1 5 cm 1.33 cm 1.35 Iron #2 4.56 cm 2.52 cm 1.56 cm (For objects floating in water.) Material Width (cm) Other (cm) Wood Height (cm) Diameter or Length (cm) #1 1.58 cm 3.62 cm 3.63 cm Cork #2 1 3.70 cm 4.49 cm 3.5 cm TABLE #3- Record the beaker or graduated cylinder measured volumes in the table below. (1 cm )= 1 mi) For objects completely submerged in water.) Material Initial volume (cm ') Vi Final volume (cm ') V Volume displaced (m') (Va = Vr-V.) Copper #1 250 cm^3 6.08 cm^3 -2.4392 m^3 Iron #2 250 cm^3 6.39 cm43 -2.4361 m43 (For objects floating in water.) Material Initial volume (cm ') V, Final volume (cm ) Vr Volume displaced (m') (Va = Vr-V.) Wood #1 250 cm43 6.20 cm43 -2.438 m^3 Cork #2 250 cm43 6.15 cm43 -2.4385 m43 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') Copper #1 0.0005886 m^3 Iron # 2 0.0022563 m43 For objects floating in water.) Wood Material Volume (m') #1 0.0008829 m^3 Cork #2 0.0090252 m^3 TABLE #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') Copper #1 0.0695 m^3 Iron #2 0.2274 m43 For objects floating in water.) Wood Material Volume (m3) #1 0.2076 m^3 Cork #2 1.865 m^3 Calculations & 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.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