Question

I need help with lab this week. I have posted theory and procedures to the lab. The questions with ????????? are the ones I need help with. Please Help!! Thank you

Theory

Density is defined as mass per unit volume that has a metric unit of kg per cubic meter. Grams per cubic centimeter i.e. g/cm3 actually is widely used as the unit of density. The densities for objects with regular shapes are easily to be determined. For objects with irregular shapes since their volume is very difficult to be determined, Archimedes’ principle is a simple method to be used to determine their densities.

Archimedes’ principle states: a body immersed in a fluid is buoyed up by a force that equals the weight of the displaced fluid. Taking the buoyancy as FB, the volume of the displaced liquid as VL, and the weight density of displaced liquid as dL, then from FB = VL dL, we have

VL = FB/dL.
If the liquid is regular water that has a density of 1 gram/cm3, and FB is measured in units of grams, the magnitude of volume is equal to FB in units of cm3. Thus by measuring the buoyant force FB, the volume of an object immersed in water can be determined, no matter how irregular the shape of the object.

Consider now an object that sinks in water. If its true weight (measured in grams for this lab) in air is WA, while its apparent weight (the weight in water) is WW. Then the buoyancy is

FB = WA – WW.

This buoyancy numerically is the volume of the displaced water, and it is also the volume of the submerged object. If the mass of a object is measured in grams which is equal to WA, then the density of the object is:

d = mass/volume = WA/(WA – WW).   Part A: Determine density of a metal block

Procedure:
Part A: Hang the aluminum block from the balance by a thread to get the true weight of WA. Then sink it in water to get the apparent weight (the weight in water) WW. Use formula (1) to get the density. The true value of density for aluminum is 2.7 g/cm3.


Part B: Determine density of a plastic cylinder

Since the density of plastic is less than that of water, it will not totally immerse beneath the water. A sink with a weight of WSA (also this is its mass numerically) is needed. The density formula will be modified as:

d = WPA/{[(WP + WS)A – (WP + WS)W] – (WSA – WSW)},         (2)

where WPA is the weight (also the mass numerically) of the plastic cylinder in air, (WP +
WS)A is the total weight of the sinker and the plastic cylinder ( they are tied together) in air, (WP + WS)W is the total weight of the sinker and the plastic cylinder in water. WSA is the weight of sinker itself in air, while WSW is the weight of sinker itself in water. The true value of density for the plastic cylinder is: 0.95 g/cm3.


Part C: Determine density of alcohol

The density of a liquid also can be determined by using Archimedes’ principle from weighing an object (using the sinker). The formula is:

d = (WSA – WSL)/(WSA –WSW)
where WSL the weight of sinker in the alcohol. The true value of density for alcohol is: 0.86 g/cm3.

Questions:

Part A) An aluminum cylinder is hung from the balance beam by a thread to get the true weight of W_A.

The aluminum cylinder is submerged in water to get the apparent weight (the weight in water) W_W.

Calculate the Density_Aluminum using the relationship:

W_A = 61.8 grams

W_W = 39 grams

The true value of density for aluminum is 2.7 g/cm³.

Density =??????????

Part 2A) Calculate the Percentage of Error_Aluminum using the following relationships.

Use the Theoretical Value for Density_Aluminum and the value you calculated for Density_Aluminum from the lab.

Density _Aluminum =

|TV - EV| / TV = ???????????

Part B). Since the density of plastic is smaller than that of water, it will not totally immerse underneath the water.

A sink with a weight of W_SA (also this is its mass numerically) is needed.

The density formula will be modified as:

where W_PAis the weight (also the mass numerically) of the plastic cylinder in air, (W_P + W_S)_A is the total weight of the sinker and the plastic cylinder ( they are tied together) in air, (W_P + W_S)_Wis the total weight of the sinker and the plastic cylinder in water. W_SAis the weight of sinker itself in air, while W_SWis the weight of sinker itself in water.

W_PA = 22.5 grams

W_SA = 69.7 grams

W_SW = 61.5 grams

(W_P + W_S)_A = 92.2 grams

(W_P + W_S)_W = 60.0 grams

The true value of density for the plastic cylinder is: 0.95 g/cm³.

Density = ????????????

Part 2B) Calculate the Percentage of Error_Plastic using the following relationships.

Use the Theoretical Value for Density_Plastic and the value you calculated for Density_Plastic from the lab.

Density _Plastic =

|TV - EV| / TV = ???????????

Part C) The density of a liquid also can be determined by using Archimedes’ principle from weighing an object (using the sinker).

The formula is:

where W_SLthe weight of sinker in the alcohol.

W_SL = 62.7 grams

The true value of density for alcohol is: 0.86 g/cm³.

Density = ?????????????

Part 2C) Calculate the Percentage of Error_Alcohol using the following relationships.

Use the Theoretical Value for Density_Alcohol and the value you calculated for Density_Alcohol from the lab.

Density _Alcohol =

|TV - EV| / TV = ?????????????

WA Marne (H) Volume(WA-Ww) Theoretical Value-Experimental Value Theoretical Value x 100% WPA Theoretical Value-Experimental Value Theoretical Value x 100% (WsA-WSL) Theoretical Value-Experimental Value Theoretical Value x 100%

Answer 1

WA Marne (H) Volume(WA-Ww)

W_A = 61.8 grams

W_W = 39 grams

The true value of density for aluminum is 2.7 g/cm³.

Density =??????????

$\rho = \frac{W_A}{W_A - W_W} \\ \rho =\frac {61.8}{61.8 - 39} = 2.71$

Density = 2.71 g/cm^3 <---------Answer to part A

Part 2A) Calculate the Percentage of Error_Aluminum using the following relationships.

Use the Theoretical Value for Density_Aluminum and the value you calculated for Density_Aluminumfrom the lab.

percentage error =

Theoretical Value-Experimental Value Theoretical Value x 100%

|TV - EV| / TV = ???????????

percentage error = $\frac {|2.71 - 2.7|}{2.71} \times 100 = 0.36$

Part B). Since the density of plastic is smaller than that of water, it will not totally immerse underneath the water.

A sink with a weight of W_SA (also this is its mass numerically) is needed.

The density formula will be modified as:

WPA

where W_PAis the weight (also the mass numerically) of the plastic cylinder in air, (W_P + W_S)_A is the total weight of the sinker and the plastic cylinder ( they are tied together) in air, (W_P + W_S)_Wis the total weight of the sinker and the plastic cylinder in water. W_SAis the weight of sinker itself in air, while W_SWis the weight of sinker itself in water.

W_PA = 22.5 grams

W_SA = 69.7 grams

W_SW = 61.5 grams

(W_P + W_S)_A = 92.2 grams

(W_P + W_S)_W = 60.0 grams

The true value of density for the plastic cylinder is: 0.95 g/cm³.

Density = ????????????

$\rho = \frac{22.5}{92.2 - 60.0 - 69.7 +61.5} = 0.9378 g /cm^3$

Part 2B) Calculate the Percentage of Error_Plastic using the following relationships.

Use the Theoretical Value for Density_Plastic and the value you calculated for Density_Plastic from the lab.

percentage error =

Theoretical Value-Experimental Value Theoretical Value x 100%

|TV - EV| / TV = $\frac{|0.9378 -0.95|}{0.9378} \times 100 = 1.3$

Part C) The density of a liquid also can be determined by using Archimedes’ principle from weighing an object (using the sinker).

The formula is:

(WsA-WSL)

where W_SLthe weight of sinker in the alcohol.

W_SL = 62.7 grams

The true value of density for alcohol is: 0.86 g/cm³.

Density = ?????????????

$Density = \frac {(69.7 - 62.7)}{(69.7 - 61.5)} =0.853 g /cm^3$

Part 2C) Calculate the Percentage of Error_Alcohol using the following relationships.

Use the Theoretical Value for Density_Alcohol and the value you calculated for Density_Alcohol from the lab.

percentage error =

Theoretical Value-Experimental Value Theoretical Value x 100%

|TV - EV| / TV = ?????????????

|TV - EV| / TV = $\frac{|0.853 -0.86|}{0.853} \times 100 = 0.8$