## Measuring Acceleration

### Robert Rosen

#### Description

Students observe, measure, and calculate acceleration. They construct an accelerometer to make measurements.

#### Objectives

The student knows that all motion is relative to whatever frame of reference is chosen and that there is no absolute frame from which to observe all motion.

The student knows that any change in velocity is an acceleration.

The student knows that investigations are conducted to explore new phenomena, to check on previous results, to test how well a theory predicts, and to compare different theories.

-Stopwatch
-Car
-Protractor
-Washer

#### Preparations

A discussion of motion, velocity, and acceleration may be necessary prior to this activity. The instructor should introduce the concept of acceleration starting with examples of motion in a straight line. In straight line motion, an object accelerates whenever it speeds up or slows down. Next, explain that an object following a circular path is accelerating, even if its speed is constant. This is true because the direction of motion changes continuously on a circular path.

#### Procedures

Knowledge/Skills:
Students will
-compare and contrast speed, velocity, and acceleration.
-know that a change in velocity is acceleration
-demonstrate an ability to measure and calculate time, velocity, and acceleration.
-utilize mathematical skills to measure and quantify acceleration.
-utilize laboratory techniques to assist in concept development.
-utilize reading and writing skills to aid in concept development.

Procedure:
1. Students work in groups of two or three, and need access to a car. Since safety is an important issue, a parent should do the driving while students take the measurements. Common sense needs to prevail; therefore, a lightly traveled road should be used perhaps early on a weekend morning. Speeds should be safe. Accelerations should be small. The parent needs to pay attention to driving while the students concentrate on taking measurements.

2. This activity uses an accelerometer to make measurements. The accelerometer needs to be constructed prior to this activity.

An accelerometer consists of a washer hanging from a thread that is fastened to a protractor as shown in the attached file, Figure A. Suppose the student holds the protractor inside a moving car. If the thread hangs vertically, then the acceleration of the car is zero. The car is moving on a straight line at constant speed. If the car is accelerating, then the direction of the acceleration is oppposite to the direction of the washer movement.

The magnitude of the acceleration is given by a=g Tan O, where O is the angle that the thread makes with the vertical as shown in the attached file, Figure B. The edge of the accelerometer must be parallel to the acceleration. This means the edge is held parallel to the car’s path if the car travels in a straight line. The edge is held perpendicular to the car’s path if the car travels in a circular path. Remind students that in circular motion, an object’s velocity is tangent to its path, but its acceleration is directed toward the center of the circular path. The instructor may wish to present proof that the statements given above are correct. If this is done, then the instructor should plan on spending several class periods carefully developing the definition of acceleration and the consequences of the definition. In particular, acceleration in circular motion is a difficult topic for most students.

3. Students study three cases.
a. The car speeds up while traveling in a straight line.
b. The car slows down while traveling in a straight line.
c. The car travels on an unbanked curve at constant speed.

4. Have students make necessary measurements. Students measure the following quantities for each case.
a. When the car speeds up from rest at a constant rate while traveling in a straight line, measure the final speed, the time for the acceleration, and the accelerometer angle O.
b. When the car slows to a stop at a constant rate while traveling in a straight line, measure the initial speed, the braking time, and the accelerometer angle O.
c. When the car travels at constant speed on a circular path, measure the constant speed. Devise a method to measure the radius of the car’s path or make a good estimate of the radius.

Remind students to convert all English units into metric units before using the formulas:
a = (vf - vi) ÷ -t (motion on a straight line) and
a = v2 ÷ r (motion on a circle)
[Note: f and i are subscripts; 2 is a superscript]
to calculate the car’s acceleration. Of course, students will want to compare each acceleration they compute using the appropriate formula to the value found using the accelerometer.

5. Students organize information themselves. A laboratory report is suggested. Share the -Measuring Acceleration Laboratory Report Rubric- provided in the attached file with the students. The report should contain a brief description of the procedure used to collect the data, the data itself, all calculations, conclusions that the student infers from the data, and sources of experimental error.

[Note: The O which refers to the angle in the above procedures should have a line drawn horizontally through it as in Figure B in the attached file. It is not possible to create this symbol, nor subscripts and superscripts, on this site.]

#### Assessments

The laboratory report may be used as a source of assessment. A suggested rubric is provided in the attached file.

The following questions may also be used to assess student understanding.

1. Any change in velocity may be called:
a. Speed
b. Tme
c. Acceleration
d. Distance

(Answer c: Acceleration is defined as a change in velocity.)

2. A car starting from rest has a constant acceleration of 4 m/s2 [2 is superscript]. How far will it go in 5 seconds?
a 25 meters
b. 50 meters
c. 75 meters
d. 100 meters

(Answer b: Distance = 1/2at2) [2 is superscript]

Additional acceleration problems are recommended. Problems using the accelerometer are also suggested.

Self Reflection:
The measurement called for in this activity probably seemed simple when the assignment was described. Were the measurements as easy to take as you originally thought? Has your view of what scientists do changed as a result of your experiences measuring acceleration?

#### Extensions

Enhancement:
Using research materials, students may investigate the escape velocity of rocket vehicles, and determine the acceleration necessary to achieve this velocity in a short period of time.

#### Attached Files

Illustrations for making and using the accelerometer and a rubric for assessing the lab report.     File Extension: pdf