Mr.José Popoff Instituto Cristiano Bilingüe Sunshine José A. Miranda Physics Class 10th Grade Measurements September 24, 2012 th DIMENSIONS I N T R O D U C T I O N th Density is the mass of a specific volume of matter. It is usually described by the formula. Small volumes of solids are usually measured in cubic centimeters, while volumes of fluids are measured in milliliters. INSTRUMENTS AND METHODS Mass is measured on a laboratory balance or a triple-beam balance.

Length is measured with a metric ruler.

Fluid Volumes are measured with a graduate cylinder. The two methods to find volume are: The linear-measurement method: Consists in making careful linear measurements of a regularly shaped object(cube, cylinder,etc.), and then use those measurements to calculate its volume in cubic centimeters. Simply substitute the measurements into the appropriate formula and sole the formula for volume.

The water-displacement method: This method is used with irregular objects, consists i filling a graduated cylinder with a predetermined volume of liquid, add the solid object, and determine the change in liquid level. In this report I will talk about how my team and I performed several steps to find the lenght, mass, and volume of a aluminum cylinder, but independently.

With the obtained measurements we had to find the volume of the aluminum cylinder, we used both method, linear-measurement and water-displacement.

When we obtained the volume and mass we had to find the density of the cylinder.

Having already all this measurements we had to find the percent error and the mean absolute deviation for density.

NOTE: The whole group did this step independently, so we had different measurements. Use various laboratory measuring techniques to collect data.

Read to the proper precision the scales on various kinds of laboratory instruments.

Organize data into useful tables.

Use significant digits in arithmetic calculations.

Perform basic statistical calculations for accuracy and precision. O B J E C T I V E S The list of materials used in this lab activity were the followings: M A T E R I A L S Triple-beam balance Aluminum Cylinder Graduated Cylinder, 100mL Metric Ruler String Water The steps to follow in this lab activity are the followings: P R O C E D U R E 1. We measured the lenght and the diameter of the aluminum cylinder. We recorded in Table 1.

NOTE: We measured the cylinder independently, until the whole group had finished measuring, we shared our results. 2. WIth the aid of the triple-beam balance we weigh the mass the cylinder. We recorded the mass in grams in Table 1. 3. We poured water into the graduated cylinder to some easily read mark. We recorded the volume (in milliliters) as the initial volume in Table 1. 4. We tied a string to the cylinder and gently lower the cylinder into the water. We recorded the volume (in milliliters) as the final volume in Table 1. 5. After doing the preceding steps (3 and 4), the whole group compared the difference in the volume from step 3 with that from step 4. R E S U L T S Table 1 Student Name Linear-Measurement 1. Ligia 2. Luis 3. Marce 4. Jose Length Diameter Mass Initial Volume (Vi) Final Volume (V ) Water-Displacement 4.98cm 5.11cm 4.99cm 4.98cm 1.22cm 1.22cm 1.21cm 1.21cm 16.88g 16.81g 16.78g 16.23g 20.1 mL 20.1 mL 20.1 mL 20.1 mL 26.6 mL 26.1 mL 26.6 mL 26.4 mL 1. We calculate the volume (V ) of the cylinder in cubic centimeters from the lenght and diameter measurements. POSTLAB EXERCISES This is the formula I used: V = πr h 1 1 2 V = pi (0.605 ) 4.98

V = 5.7 cm 1 1 2 3 2. Each of our team members recorded the values for V1 in Table 2. 3. We determine the displacement volume (V2) using the Vi and the Vf measurements in Table 1: V = V - V f 2 f i V = 26.4 - 20.1

V = 6.2 mL The whole team recorded V2 in Table 2. 4. We calculate the Method 1 density using V1 from Table 2 and mass from Table 1. Each member recorded the value in Table 2 as p , then we calculate the average of the group. 1 5. We calculate Method 2 density using V2 from Table 2 and mass from Table 1. Then each member recorded the value in Table 2 as p , then we calculate the average of the group. 2 6. We determine the ''percent error'' in our density measurements and calculations for each of our group member average. The formula we used was: percent error= (experimental value - accepted value) accepted value (2.64 g/cm ) x 100% R E S U L T S Table 2 Linear-Measurement

(Method 1) Student Name 1. Ligia 2. Marce 3. Luis 4. Jose Average V 1 5.8 cm 3 5.7 cm 5.9 cm 5.7 cm 3 3 3 5.8 cm 3 p 1 2.9 g/cm 2.9 g/gm 2.8 g/cm 2.8 g/gm 2.9 g/cm 3 3 3 3 3 Percent Error 9.8 % 6.1 % 9.8 % 6.1 % 7.9% Water-Displacement

(Method 2) V 2 6.5 mL 6.5 mL 6.0 mL 6.2 mL 6.3 % p 2 2.6 g/cm 3 2.6 g/cm 2.8 g/cm 2.6 g/cm 2.7 % Percent

Error -1.5 % -1.5 % 6.1 % -1.5 % 0.4 % 7. Now we can calculate the mean absolute deviation of our results: a. From Table 2, we located the density for Method 1 for each of our group members(p1). Then we located the average density for Method 1 for the group from Table 2.

b. We found the absolute value of the differences of p1 and p1 av for each of our group member and recorded in Table 3.

c. We determine the average of these differences and recorded in Table 1. This is the mean absolute deviation for our group for Method 1. We used absolute values.

d. We repeated this process for p2 and p2 av. This is the mean absolute deviation for Method 2. 8. We calculate the percent differences between the densities determined by the two methods: a. We located p1 and p2 for each group member on Table 2. We used this equation: percent difference= p - p 1 2 p + p 1 2 2 ( ) X 100% b. We recorded the values in the last column in Table3 and their average. R E S U L T S Table 3 Student Name p - p 1 1 av 1. Ligia 2. Luis 3. Marce 4. Jose Average p - p 2 2 av Percent Difference Between Methods 0 g/cm 0 g/cm -0.1 g/cm -0.1 g/cm 0.05 g/cm 3 3 3 3 3 -0.1 g/cm 3 3 0.1 g/cm -0.1 g/cm 3 -0.1 g/cm 3 0.1 g/cm 3 10.9 % 0 % 10.9 % 7.4 % 7.3 % Formula: p=m/v

p=16.23/5.7

p=2.8 g/cm We used the same formula from Method 1 density. 3 3 1. What is the accuracy of your group for Method 1?

Answer= 7.9 %

2. What is the accuracy for Method 2?

Answer= 0.4 %

3. What is the mean absolute deviation of your group for Method 1?

Answer= 0.05 %

4. What is th mean absolute deviation of your group for Method 2?

Answer= 0.1 %

5. What is the average percent difference for your group?

Answer= 7.3 % DATA ANALYSIS 6. Which of the two methods produced results nearer to the accepted value for the density of your metal sample? Why? Answer= Method 2, first of all the water-displacement method give us more exact results to the actual value than the linear-measurement method and with Method 2 all the results we obtained were nearer to the accepted value. 7. If the precision of your group is good but the accuracy is poor, what would you expect the most likely source of error to be--human or equipment? Explain. Answer= If we have good precision but poor accuracy I think it would be equipment error because maybe the balance was not well calibrated or the table in which we performed the activity was not straight, and I think that is not possible that the whole group made the same mistake. 8. If the accuracy of your group is good but the precision is poor, what would you expect the probable source of the discrepancy to be--human or equipment? Explain the reason for your choice and identify what part of the procedure was done to reduce this problem. Answer= If we have good accuracy but poor precision I think it would be human error because maybe we didn't measured well the length or we were not well seated and we could not see the exact measurement of the volume, or simply we did not apply well significant digits. 9. As noted above, there are two likely sources of error in this experiment--human and equipment.

List at least three examples of human error. Answer= We can move the table.

We can do or calculate bad something in the procedure.

We can not apply the right formula. 10. List at least two potential equipment errors that could contribute to a lack of accuracy. . Answer= Equipments can be rusted.

Using a ruler of 100 cm to measure 120 cm. 11. Discuss a potential problem when determining the density of a porous object using the water- displacement method. Answer= I think that the major problem would be that the porous object would absorb the water from the graduated cylinder. 12. Discuss a problem with using the water-displacement method to determine the density of an object that is less dense than water. Answer= Well, first of all the biggest problem would be that the object would float instead of sink and we could not be able to state the differences between the first volume of the graduated cylinder without the object and the second volume with the object inside the graduated cylinder, so we could not be able to subtract the two volumes. Water-displacement Method gives results to the nearer actual value. C O N C L U S I O N With the water-displacement Method we had a high accuracy and precision. With the linear-measurement Method we had a high precision but a poor accuracy. Human errors are more common in measurements than equipment errors. We learned how to calculate density with different methods. We learned how to find the percent error, percent differences and the mean absolute deviation.

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# Physics Lab Report

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