procedure

A. Length:

1.      Estimate the length of a meter by putting a pen or pencil at one end of a table and then placing a second pen or pencil about one meter away from the first.

2.      Using your meter tape measure the actual length of your meter estimate.

3.      Record the length of your meter estimate.

4.      Calculate the percent error of your estimated meter from the actual meter.

B. Time:

1.      Estimate a 30 second time period while someone else times you using a stopwatch. (If you don’t have a partner, you can do this experiment by closing your eyes; start the stopwatch and stop it when you think 30 seconds have elapsed.)

2.      Record the actual time of your estimate.

3.      Calculate the percent error of the estimate to the actual time.

C. Mass:

1.      Pick up a small paperback book or similar small object and estimate it’s mass.

2.      Determine the actual mass of the object using your 500-g spring balance.

3.      Record the estimated mass and the actual mass and calculate the percent error.

Question:

Why is it important for you to have a “feel” for length, time, and mass?

2. Measurements Using Instruments of Various Degrees of Precision:

For recording data set up data tables for each of the three items you will measure below.

Description of Object Measured:             

Measurement of your hand span: ________ cm

A. Your hand:

1.      Spread out your hand and measure the distance from the tip of your thumb to the tip of your little finger in centimeters.

2.      Record this measurement on your data sheet.

3.      Now use your hand to measure the length, width, and height of three rectangular items such as small books, shoeboxes, or similar. The objects should weigh less than 500 g, so you can also determine the mass if you wish.

4.      Record these measurements in hand units on your data sheet.

B. Metric ruler and meter tape:

1.      Use the metric ruler to measure the length, width, and height of the same objects from Step A and record the measurements in centimeters. Be sure to place the markings on the ruler directly against the object to minimize the possibility for error. Since the ends of the rulers are often worn a bit, start your measurements at the one centimeter mark, then count the units rather than relying on the numbers marked on the ruler.

2.      Record your measurements to the nearest half millimeter. All your measurements should have two places to the right of the decimal point and thus end with either a 5 or a 0, i.e., 12.35 centimeters or 9.60 cm.

3.      Measure the length, width, and height of the box with the meter tape.

4.      Record all measurements on your data sheet. Units should be in centimeters and recorded to the nearest half millimeter as before.

C. Calculations:

1.      Convert the hand units to centimeters and record.

2.      Find the volume of the object using the three different sets of measurements. Remember, the volume of a rectangular box is: v=length x width x height. You must show the units, cubic centimeters, when recording calculated volume. 

Questions:

A. Can you think of an occasion when it would be adequate to use your “hand”

measurement?

B. What would happen to your volume calculations if the length, width and height

measurements were off a little?

3. Graphing data and the determination of π:

A.    Select five circular objects of different sizes, such as an AAA battery, a crew cap from a soft drink bottle, the cardboard center of a paper towel roll, cups of various sizes, plates of various sizes, etc.

B.  Using the metric ruler or meter tape measure the diameter, d, in centimeters to two decimal points and record.

A.    Using the meter tape measure the circumference, C, in centimeters of each object to two decimal points and record.

D.  Graph C vs. d using a computer spreadsheet program.

E.  Use the linear fit command from the menu to plot a best-fit line. Remember, the equation for the slope of the line is, y = mx + b, where the slope is m.

F.      What is the slope of the line? What does it represent?

G.    Calculate the percent error of your value from the true value.

4. Density Measurements:

Determine the density of q metal bolt (or any irregular metal object) by the water-displacement method:

A.    Half-fill the graduated cylinder and record the volume of the water without the object.

B.     Place the metal bolt into the graduated cylinder and record the new volume. The difference between the two volumes represents the volume of the bolt or object.

C.     Tie a string around the metal bolt and attach the string to the bottom of the 10-g spring scale so that the bolt hangs down about 5 cm. Record the bolt’s mass in air.

5. Determine the density using Archimedes’ Principle:

A.    Partially fill a cup with water.

B.     While holding the top of the 10-g spring scale, suspend the metal bolt hanging from a string into the partially filled cup of water. Make sure that the bolt doesn’t touch the sides or bottom of the cup.

C.     Read the 10-g spring scale. This is the bolt’s mass in water. Record it.

D.    Subtract the bolt’s mass in water from the bolt’s mass in air (recorded in 4.C above). This is the apparent mass lost in water.

E.     To calculate density, divide the bolt’s mass in air by the bolt’s apparent mass lost.

Question:

Which of the two volume determinations will be more accurate? Why?

6. Time measurements:

A.    Measure and mark a vertical distance of two meters from the floor up.

B.     Stand on a chair and hold a small box or similar object at the marked height in one hand and the stopwatch in the other hand.

C.     Start your stopwatch at the same instant you release the object and stop the watch when you hear the box hit the floor. Record the time to the nearest tenth second. Repeat three times. Units will be seconds. If you have an assistant, have the assistant time you while you drop the box – use verbal commands like “start” or “now” to synchronize the dropping and timing.

D.     Find the average drop time of the object and record it in seconds. 

E.                 Repeat this experiment with your eyes closed.

Question:

Do you think the average drop time is more accurate than any of the individual drop times? Sometimes many trials are run and recorded. Then the highest and lowest data points are disregarded when taking the average. Could this technique help in this experiment? How?