Physics lab

Lab Manual Irina Golub

July 30, 2017

PURPOSE

In this experiment, experience is gained in performing measurements and in making calculations using these units. Learn how to assess the uncertainty in a measurement. Learn how to decrease the uncertainty in the measurement (that is, increase the accuracy) of something that repeats in a regular way.

INTRODUCTION

Read the theory for Lab #1:

 University Physics Volume 1Chapter #1:| UNITS AND MEASUREMENT  Statistic.pdf

MATERIALS

• a 12-inch ruler with metric rulings on the back (e.g., centimeters and millimeters) • a yardstick with metric rulings on the back, or a meter stick • a book • a room with a flat ceiling

PART ONE: CALCULATING THE VOLUME OF A BOOK IN CUBIC METERS

1.) Measure the length L. of your book to the nearest millimeter at three different locations on the book (see Figure 1), and record these values on your data table.

2.) Measure the width W of your book to the nearest millimeter at three different locations on the book(see Figure 1), and record these values on your data table.

3.) Measure the thickness T of your book to the nearest millimeter at three different locations on the book(see Figure 1), and record these values on your data table.

Figure 1

A Pictorial Representation of the Top of Your Book

Figure 1: A Pictorial Representation of the Top of Your Book

Data

Measure and record the length of each side of a textbook or other book, to the nearest millimeter.

Calculations

1. Using your measurement data, calculate the arithmetic mean 𝐿𝐿�⃗ for the length of your table top, and record this value on your data table.

2. Using your measurement data, calculate the arithmetic mean 𝑊𝑊���⃗ for the width of your table top, and record this value on your data table.

3. Using your measurement data, calculate the arithmetic mean 𝑇𝑇�⃗ for the thickness of your table top, and record this value on your data table.

4. Using your measurement data, calculate the standard deviation of the length of your book top 𝜎𝜎𝑙𝑙 and record this value on the data table.

5. Using your measurement data, calculate the standard deviation of the width of your book top 𝜎𝜎𝑊𝑊 and record this value on the data table.

6. Using your measurement data, calculate the standard deviation of the thickness of your book top 𝜎𝜎𝑇𝑇 and record this value on the data table.

7. Calculate the relative error of your measurement of the length of your book top 𝜀𝜀𝑙𝑙 and record this value on the data table.

8. Calculate the relative error of your measurement of the width of your book top 𝜀𝜀𝑊𝑊 and record this value on the data table.

9. Calculate the relative error of your measurement of the thickness of your book top 𝜀𝜀𝑇𝑇 and record this value on the data table.

10. Using your data, calculate the best estimate of the area of your book top A and determine the best estimate of the error of this measurement a, 𝜎𝜎𝑡𝑡𝑡𝑡𝑡𝑡 𝑎𝑎𝑎𝑎𝑑𝑑 𝑟𝑟ecord these values on the data table.

11. Using your data, calculate the best estimate of the volume of your book V and determine the best estimate of the error of this measurement a, 𝜎𝜎𝑣𝑣𝑡𝑡𝑙𝑙 𝑎𝑎𝑎𝑎𝑑𝑑 𝑟𝑟ecord these values on the data table.

12. Using the data you measured for each side of the book, calculate the volume of the book in cubic meters.

Length Data

i 𝐿𝐿𝑖𝑖 𝑑𝑑𝑖𝑖,𝑙𝑙 |𝑑𝑑𝑖𝑖,𝑙𝑙|^2 1 2 3 4 5 6 7

𝐿𝐿� = 1 𝑁𝑁 �𝐿𝐿𝑖𝑖

𝑁𝑁

𝑖𝑖

𝜎𝜎𝑖𝑖,𝐿𝐿 = � 1 𝑁𝑁 �� |𝑑𝑑𝑖𝑖,𝑙𝑙|^2

𝑁𝑁

𝑖𝑖

Where, 𝑑𝑑𝑖𝑖,𝑙𝑙 = 𝐿𝐿𝑖𝑖 − 𝐿𝐿�

𝜀𝜀𝐿𝐿 = 𝜎𝜎𝑖𝑖,𝐿𝐿 𝐿𝐿�

Width Data

i 𝐿𝐿𝑖𝑖 𝑑𝑑𝑖𝑖,𝑊𝑊 |𝑑𝑑𝑖𝑖,𝑊𝑊|^2 1 2 3 4 5 6 7

𝑊𝑊� = 1 𝑁𝑁 �𝑊𝑊𝑖𝑖

𝑁𝑁

𝑖𝑖

𝜎𝜎𝑖𝑖,𝑊𝑊 = � 1 𝑁𝑁 �� |𝑑𝑑𝑖𝑖,𝑊𝑊|^2

𝑁𝑁

𝑖𝑖

Where, 𝑑𝑑𝑖𝑖,𝑊𝑊 = 𝑊𝑊𝑖𝑖 −𝑊𝑊�

𝜀𝜀𝑊𝑊 = 𝜎𝜎𝑖𝑖,𝑊𝑊 𝑊𝑊�

Thickness Data

i 𝐿𝐿𝑖𝑖 𝑑𝑑𝑖𝑖,𝑇𝑇 |𝑑𝑑𝑖𝑖,𝑇𝑇|^2 1 2 3 4 5 6 7

𝑇𝑇� = 1 𝑁𝑁 �𝑇𝑇𝑖𝑖

𝑁𝑁

𝑖𝑖

𝜎𝜎𝑖𝑖,𝑇𝑇 = � 1 𝑁𝑁 �� |𝑑𝑑𝑖𝑖,𝑇𝑇|^2

𝑁𝑁

𝑖𝑖

Where, 𝑑𝑑𝑖𝑖,𝑇𝑇 = 𝑇𝑇𝑖𝑖 − 𝑇𝑇�

𝜀𝜀𝐿𝐿 = 𝜎𝜎𝑖𝑖,𝑇𝑇 𝑇𝑇�

PART TWO: CALCULATING THE VOLUME AND WEIGHT OF THE AIR IN A ROOM

Data

1. Measure and record the length and width of a room that has a flat ceiling at three different locations. Estimate the ceiling height of the room without actually measuring it.

2. Make a guess of the weight of the air in the room and record your guess.

3. Find, using your textbook or an internet search, the density of air in units of kilograms per cubic meter.

4. Create the data table and enter your measurements.

Calculations

1. Calculate the volume of the room in cubic meters. 2. Determine the best estimate of the error of this measurement. 3. Convert the density of the air you found in kilograms per cubic meter to Newtons per

cubic meter by multiplying by “g”, the acceleration due to gravity, i.e., 9.8 m/s^2. The density of air in kilograms per cubic meter is called a mass density because it is mass divided by volume. The density of air in Newtons per cubic meter is called a weight density because it is weight divided by volume.

4. Calculate the weight of air in the room in Newtons by multiplying the weight density of air you calculated in #3 (in Newtons per cubic meter) by the volume of air (in cubic meters) you calculated in #1.

5. Determine the best estimate of the error of this measurement 𝑎𝑎𝑎𝑎𝑑𝑑 𝑟𝑟ecord the value on the data table.

6. Convert the weight of air in the room that you calculated in #4 from Newtons to pounds and record your result. Does the weight of the air in the room (in pounds) surprise you?