## Finding the Acceleration Due to Gravity

### Phil LeeBay District Schools

#### Description

This is a laboratory exercise which is used to calculate the acceleration due to gravity.

#### Objectives

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Selects and justifies alternative strategies, such as using properties of numbers.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

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

#### Materials

-Supplies needed:
-Strips of carbon paper (1in. wide by 2 in. long)
-Long strip of paper (3/4 in wide by 36 in. long)
-Tuning fork of known frequency
-Tape
-Measuring instrument (ruler, meter stick)
-Paper clip (to attach weight to paper…paper should have tape around end and small hole for the paper clip
-Small weight (small fishing lead..1/2 oz. or whatever is available)

#### Preparations

1. Gather materials…the hardest part might be finding tuning forks, you might try your district media center.
2. Cut long strips of paper, you might start with a roll of paper from an adding machine or maybe get a length of butcher paper...maybe from the art teacher.
3. Cut strips of carbon paper.
4. Make copies of lab setup and Acceleration Lab Worksheet.

#### Procedures

1.Start by standing in front of the class and dropping an object usually a textbook is very effective). Ask the students what happened. Point out that the instant you released the item, it was stationary, then started moving downward. The speed (velocity) increased and continued to increase until it hit the floor.

2. Ask if any can define velocity, and acceleration. Review acceleration and velocity. If they do not recall definitions and\or formulas, write those on the board . Note that any change in velocity is caused by an acceleration. (Terminal velocity and effects due to air resistance might be discussed later.) (Students will be graded on their ability to reproduce the acceleration formula on the worksheet.)

3. Ask if anyone knows the value for acceleration due to gravity. Tell them we are going to do a laboratory exercise which will help them calculate the acceleration due to gravity.

4. Pass out lab materials and go over lab procedures:
(Refer to associated file for setup graphic) Model the lab and leave it setup for the students to refer to if necessary. It would help if copies of the setup graphic were distributed to the groups. Students should work in groups of 2-3.

5. Lab setup:
A piece of carbon paper is taped to the edge of a counter ( just loose enough so that another piece of paper will slip behind it and the counter).The long strip of paper should be folded (1/2 inch folds) a couple of times and then taped to add strength. Straighten out the paper clip and bend a short hook on one end and attach the weight on the other end. Carefully push the hooked end through the taped end of the paper.The other end of the paper is then passed upward between the carbon paper and the counter such that the weight hangs just beneath the carbon paper. Check to make sure setup is correct.

6. Lab procedure:
One student holds the upper end of the long strip of paper. The tuning fork is lightly tapped and held lightly against the carbon paper. The upper end of the long strip of paper is released. As the paper slides between the carbon paper and the counter, the tuning fork should leave a row of marks on the paper. This should be practiced several times to insure clear marks on the paper.

7. Calculations:
Have students measure consecutive intervals between the dots…..use some that are spaced out enough to provide accurate measurements. Then have students perform their calculations: (Refer to page 2 of the associated file for sample calculation. You might review again the formulas and calculations and explain why velocity/acceleration can be found by multiplying by the frequency of the tuning fork.) Students will calculate velocity for each interval by multiplying the length of each interval times the frequency of the tuning fork. Students will then calculate acceleration by multiplying the difference in consecutive velocities by the frequency of the tuning fork. Students should record all measurements, list formulas and show calculations on the acceleration lab worksheet. (see associated file)

#### Assessments

(Note: This lesson does not assess all parts of the math standards listed.)

The students will be assessed from the completed worksheets. Worksheets will be graded on the correct use of formulas, calculations, and on correctly describing the increasing distances between the dots on the long sheet of paper in terms of velocity and acceleration.

--Students will receive 10% of the grade for correctly stating the formula used to calculate acceleration.

--Students will receive 10% for each correct calculation and 10% for corectly finding the acceleration in each interval.

--Students will receive 30% for correctly explaining the increased distances between the dots in terms of velocity and acceleration.

--Scoring can based on standard secondary grading scale. This assessment should be formative until students can state the formula, perform the calculations, and adequately explain the concepts. Students may need additional practice and feedback based on the results of the formative assessment.