Lab 5

The Science of Measurement

Contents

Objectives
Introduction
Equipmentt
Procedures

1. Least Count of Measuring Instruments
2. Surface Area of Desk
3. Volume of Wooden Block
4. Timing Downhill Runs
5. Measuring Pendulum Period

Questions

Learning Objectives

After completing this experiment, you should be able to do the following:

1. Define the terms accuracy, measurement, least count, precision, and significant figures.

2. Make proper measurements and record them to the correct number of significant figures using a meter stick and electric timer .

3. Calculate the area and volume when the dimensions of an object are known.

4. Measure the motion of a rolling object and compare it with a calculated value.

4. Determine experimentally and theoretically the period of a simple pendulum.

5. Distinguish between percent error and percent difference.

6. Distinguish between error and precision.

Introduction

This lab exercise has quite a bit of explanatory material, located online. Click anywhere in this paragraph to link to it. It may take you quite a bit of time to read it, but you will not be able to understand and complete this lab exercise unless you take the time to read before you begin.. This lab will also help you to get better results on lab 6.

Equipment

Meter stick, electric timer, wooden block, empty can, ramp (1.25 meter board or cardboard), simple pendulum (hex nut, string, pencil, book).

You may substitute a metric ruler in place of a meter stick, but measurement must not be made in inches.

Use a digital wristwatch with a stopwatch for the electric timer. If you don't have one you will need to buy or borrow one to use in this and subsequent experiments. Check Long's, Kmart, Costco, etc. for an inexpensive one.

Be sure to describe what type of instruments you are using as part of your lab report.

Procedures

For all procedures in this lab exercise round the measurements to the correct number of significant figures.

1. Least Count

The least count is the smallest subdivision marked on a measuring instrument.

Determine the least count of your measuring stick.

Record the numerical value of the least count and the unit of measurement.

Example: A meter stick is divided into 100 equal divisions and numbered. Each of these numbered divisions is called 1 cm. ('one centimeter' means 'one one-hundredth' of a meter). Each centimeter is further divided into 10 equal divisions. This is the smallest subdivision on the meter stick.

The least count is be expressed in two parts, a numerical value and a unit of measurement For the meter stick above the least count is stated as 1/1000 (numerical value) of a meter (unit of measurement), or as 1 (numerical value) millimeter (unit of measurement). However the least count is expressed, it must have the correct unit of measurement for the numerical value stated.

Fill in the blanks in Table 1 with the least count for your ruler.

Table 1 Least Count of Ruler Numerical Value Unit of Measurement . .

2. Surface Area of Desk

Measure the top of your desk or table and determine the surface area in square centimeters. Area is length x width. Make good measurements, estimating between the marks on the ruler as illustrated.. Round and record the answer to the correct number of significant figures.

3. Volume of Wooden Block

Determine the volume of the wooden block in cubic centimeters. Take three measurements of each dimension (length, width, height) of the wooden block and record all significant digits in Data Table 2.2. Round and record the answer to the correct number of significant figures.

4. The Downhill Run

1. Set up a ramp using a board or cardboard approximately 1.25 meters (4 ft.) long.

2. Measure the length of the board and enter the length in the data table below.

3. Using books or blocks, raise one end of the ramp to a height of approximately 0.25 meters (25 cm.). Enter the height in the table below.

4. Measure a distance of 1 meter anywhere on the ramp. Record the actual measurement in the data table below.

Be sure that all measurements are recorded to the correct number of significant figures.

You may find it helpful to place a book or block at the end of the 1 meter run. This will help you to coordinate the timing of the roll.

5. Hold a ruler or pencil to keep the can from rolling. To start the can rolling at the instant you start the timer, lift the 'starting gate' directly away from the ramp. Stop the timer when the can reaches the 1 meter mark. Record the time in the data table.

6. Repeat the timing six times. Each six 'runs' constitute a 'trial'

7. Repeat for two more trials. You should have a total of 18 times in the data table.

8. Calculate the average for each trial. (Add the six time valus and divide by 6).

9. Calculate the overall average. (Add the three trial averages and divide by 3).

The time required to roll down the ramp depends on the distance rolled (d), the height (h) and length (L) of the ramp, and the acceleration of gravity ( g = 9.8 m/s²or 980 cm/s²).

The relationship is written as:

10.Use Relationship 4 to calculate the 'standard' or 'theoretical' time required for the can to roll your distance d, using your values for L and h. Click here to see how to do the calculation.

11. Calculate the percent error and percent difference for the time t. Use the largest and smallest values of all 18 time measurements and the overall average for the percent error.

Percent Error: The accuracy of a measurement refers to how well the experimental value agrees with a standard value. The standard may be a calculated value (as with the can rolling downhill), or a generally accepted value (such as the acceleration of gravity),

Table 4.2 Percent Error in Rolling time of Can Percent error .

Percent Difference: Precision refers to the repeatability of measurements. The closer all of the measurements are to one another, the more precise they are.

5. The Period of the Pendulum

The time a pendulum takes to complete one swing is called its period.

A simple pendulum consists of a small heavy mass attached to a light string and suspended from a rigid support. The pendulum is set swinging by displacing the mass (called a bob) slightly from its equilibrium position.

The word "simple" is used to describe this pendulum because most of the mass is concentrated in the bob. (An ideal simple pendulum would be one in which the entire mass is concentrated at a point. This is impossible to obtain because a bob of any size will have a distribution of mass and even the lightest of strings has a small amount of mass.)

When you start the pendulum swinging, use a length of arc about one-tenth of the length of the pendulum length. That is, displace the pendulum bob to the side about one-tenth the value of the pendulum length (about 5 cm). Too large a displacement will cause the pendulum to vary from its 'theoretical' rate of swinging.

The period, T, is defined as the time of one complete swing of the bob. Its theoretical or standard value depends only upon its length and the acceleration of gravity. Although you might suspect that the size of the arc of its swing would affect the period it does not, at least for small arcs. Galileo's discovery of this eventually led to the invention of the pendulum clock. It can be calculated from a simple relationship.

The period of the simple pendulum depends only on its length and the acceleration of gravity. We will refer to this as "Relationship 5":

You will test this relationship in this part of this exercise as you measure the period (T) for a given length (L). You will measure the period and compare the results with the calculated value of the period

5.1 Determine the period of a simple pendulum with a length of 49.0 cm.

1. Construct the pendulum according to these instructions:

Use a small heavy object that has radial symmetry (is not elongated). A cork, a fishing weight, a hex nut, etc. will work just fine. The smaller and heavier the better. Simply tie or otherwise attach a string to it, then tie the string it to a pencil. Lay the pencil on the table so that the pendulum hangs over the edge. Weight down one end of the pencil with a heavy book so that the pendulum bob can swing freely.

Measure the length L from the center of the bob to its support. Make L as close to 49 cm. as you can, but measure the actual length to the appropriate number of significant fgures.

.

2. Write the actual measured length of your pendulum here (to the appropriate number of significant figures):

3. Perform five trials, timing ten swings each trial.

Start the pendulum swinging with a very small displacement. The smaller the arc the more accurate the relationship.

• One swing is one complete cycle, back and forth.
• Let it swing a few times before starting the count.
• Enter the data in the table below.
• Divide the time for ten swings by ten to find the period.

4. Calculate the average period using the five trials. This is your measured or experimental value for the period.

5.2 Calculate the theoretical or standard value of the period for your pendulum. Use Relationship 5 with your measured length, L. Click here to see how to do the calculation.

5.3 How accurate is the measurement of the pendulum's period?

Calculate the percent error using the theoretical (calculated) value as the standard value. Use the average of your five trials as the experimental value. Show your work.

5.4 How precise is the measurement of the pendulum's period?

Calculate the percent of difference between your largest and smallest experimental values of time for the pendulum.

QUESTIONS

1. Define "unit" and give an example of it.?

2. Distinguish between least count and significant figures

3. Distinguish between accuracy and precision. See the document entitled "Accuracy vs. Precision" if you need help.?

4. Are your calculations for area and volume rounded to the correct number of significant figures? What should be the appropriate number of decimal places for your 'ruler'?

5. Are any of the time measurements 'really' different from the others? If so, briefly explain why?

6. Why is it preferable to make multiple measurements of time?

7. Use Relationship 5 to calculate the length in centimeters of a simple pendulum that has a period of one second. See the document entitled "Pendulum Length" and substitute a value of 1 sec for T if you can't do the algebra necessary to arrange Relationship 5.

8. Distinguish between percent error and percent difference.

9. What factors might account for the accuracy and precision of the pendulum measurements compared to the ramp?

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