Lab 8 - lab assignment PDF

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Conceptual Physics Workbook Density and Archimedes’ Principle Name: ____Maggie Newman______________________ Class:__PHYS-1402 _____ Section: 101__Date:_7/16/2020 __

Purpose The purpose of this lab is to learn how to find the density of materials, and to investigate Archimedes’ principle and the buoyant force. The procedure is outlined in very general terms below. You must use your own knowledge and skills to decide how to make many of these measurements. I.

II.

Materials A. Wood block B. D. Ruler E. G. Catch Beaker H.

Metal block C. Mass Balance F. 2 N Spring Scale I.

Graduated Cylinder Overflow Beaker 5 N Spring Scale

Density Density is defined as the amount of mass in a unit of volume. So to calculate the densities of the materials below, we must know the mass of the material and the volume of the object. You will have a meter stick and a triple-beam balance to use in obtaining your measurements. Attach additional pages well organized to record intermediate data. A.

Find the density of the wood block. Mass (g) _238.6g

Density (g/cm3)__0.7581g/cm^3______

Volume (cm3) _314.7 cm^3______ B.

Find the density of the metal block. Can you identify the metal using the chart on the last page? Mass (kg)____0.085 g______________ Volume (m3)_0.000027 m^3 ____

C.

Density (kg/m3) 3148.15_kg/m^3___

Type of metal? _Aluminum ____

Find the density of 50 ml of water in the graduated cylinder. Compare it to the accepted value (you can find it in your book) by calculating the percent difference. (1 ml = 1 cm3 = 0.000001 m3)

Mass ____0.0493 kg__________________ Measured Density ___989 kg/m^3 Volume ___5E-5 m^3____ Accepted Density _1000 kg/m^3________ Percent error _____1.4%_________

III.

Archimedes’ Principle and the Buoyant Force Archimedes’ principle states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid that the object displaces. A.

Procedure 1: Using the small beakers to catch the water that is displaced when the blocks are lowered into the cans, and with careful mass measurements, the weight of the water can be determined, thus demonstrating Archimedes’ principle.

B.

Procedure 2: Another way to measure the buoyant force on the object is to compare the weight of the object dry to the weight of the object when it is submerged (but not touching the sides or bottom). In other words, FB = Wdry – Wwet It’s easy to measure force with a spring scale:

Forces acting on sample

spring scale

FB

Wwet is equal and opposite to

Wdry

C.

Procedure 3: Fill a beaker partly full of water and measure its mass. Call this mbw for mass of only the beaker and water and calculate the force the scale is exerting upward, Wbw = mbwg. Then dip the unknown in and measure the mass (submerged but not touching the sides or bottom). Call this min for mass with unknown in the beaker and water and calculate the force the scale is exerting upward, Win = ming. See the following figure to understand the force diagrams:

Forces acting on sample Wwet FB

Forces acting on beaker – by Newton’s 3rd Law, if the water is pushing up and the sample, the sample must push down with equal and opposite force. 

Wdry mass balance Therefore, here is another way to find FB: FB = Win – Wbw.

FB Wbw

Win

Observations:

Note: 1 ml = 1 cm3 = .000001 m3

Volume of metal block: _0.031__m___0.031______m __0.031_______m =_2.98E-5____m3 Procedure 1 Data: Mass of dry overflow beaker: ___0.0583________ kg Mass of overflow beaker and displaced water: ___0.0906___________ kg Mass of displaced water: _0.0323________ kg Procedure 2 Data: Weight of dry metal block: _0.88__________ N Weight of submerged block: _0.58_____ N

Procedure 3 Data: Mass of beaker and water: _0.506_ kg

Weight of beaker and water: 4.96__ N

Mass of beaker and water with sample in water: _0.537___ kg

Weight of beaker and water with sample in water: __5.27____ N

Calculations of Buoyant Force: 1) Weight of displaced water from Procedure 1: _____0.32 and 0.38___________ N 2) Buoyant force from Procedure 2: _0.3 and 0.24______ N 3) Buoyant force from Procedure 3: ___0.31 and 0.31_________________ N

1.

Compare the weight of the displaced water, and the average buoyant force on the block. How are these quantities related?

The buoyant force is equal to the weight of the displaced water.

2.

Since we are comparing more than two values, we can’t use percent difference or percent error to evaluate our uncertainty. Instead, calculate the standard deviation for your three measurements of buoyant force above. Essentially, it’s like the root-mean squared of the differences from the mean ( x ). N is the number of values you are comparing, and xi represents the individual values. List some of the possible reasons for this uncertainty. 1  =  (xi − x )2 N i 1 𝑠1 = 𝑠𝑞𝑟𝑡(( ) [(0.3165 − 0.3076)2 + (0.30 − 0.3076)2 + (0.3063 − 0.3076)2 )]) 3 1 𝑠2 = 𝑠𝑞𝑟𝑡(( ) [(0.3802 − 0.3298)2 + (0.30 − 0.3298)2 + (0.3063 − 0.3298)2 )]) 3 S1= 0.0068 N S2=0.03582 N

The possible reasons for the uncertainty could be surface tension and how it may affect the instruments used.

Write a conclusion discussing your observations. Remember to include any errors that may have occurred and how to avoid them. Do not restate data unless it is being used for reference. The goal of the Archimedes lab was to find the density and buoyancy forces of metal blocks using several methods. The density discovered led us to believe that the mystery metal is Aluminum. Sample 2 had a higher mass and thus had a higher buoyancy force than Sample 1, which makes sense because the mass and density were the same, but the volumes were different. Surface tension may be an error that occurred, however surface tension is unavoidable unless in a vacuum.

Density and Specific Gravity http://www.funphysicist.net/help/density.htm Now=9/5/2012 Mod=09/05/2012 Selected Table of Densities below -- Click here for Complete Table of Densities gm kg ρ( ) ρ( ) Solids S.G. (Specific Gravity - no units) cm3 m3 Gold (Au)

19.3

19.3

19,300

Lead (Pb)

11.3

11.3

11,300

Silver (Ag)

10.5

10.5

10,500

Copper (Cu)

8.9

8.9

8900

Brass (average)

8.6

8.6

8600

Steel (Fe)

7.8

7.8

7800

Tin (Sn)

7.29

7.29

7290

Zinc (Zn)

7.14

7.14

7140

Aluminum (Al)

2.7

2.7

2700

Balsa Wood

0.3

0.3

300

Oak

0.8

0.8

800

Earth Average

5.52

5.52

5520

Mercury (Hg)

13.6

13.6

13,600

Water Oil

1.0 0.9

1.0 0.9

1000 900

Alcohol

0.8

0.8

800

Liquids & Gases

Antifreeze

1.125 (32°F) 1.098 (77°F)

1.125 (32°F) 1125 (32°F) 1.098 (77°F) 1098 (77°F)

Air

1.29 * 10-3

1.29 * 10-3

1.29

Hydrogen

9.0 * 10-5

9.0 * 10-5

0.09

Oxygen

1.43 * 10-3

1.43 * 10-3

1.43...