Question

Simple Pendulum

Please write your answers on a color of your choice.

Purpose To determine the value of the gravitational acceleration by using a simple pendulum.

Lab goals

• To be able to perform an experiment independently.
• To be able to take measurements, obtain results, and interpret them correctly.               To be able to estimate the accuracy of experimental results.

Equipment

• A small object with a hole such as a bead or nut, and a long string
• A measuring tape (or ruler) and a watch. If you don't have a watch, you can use your cell phone to measure the passing time.
• Scissors, a pencil and a scotch tape

Theory

A simple pendulum consists of an object with negligible size hanging on a string. When the object is deflected from its equilibrium, it swings (oscillates) back and forth. The time for one complete cycle (oscillation) is called the period of oscillation, T. For small angles of deflection, the period of the simple pendulum is given by the following formula:

?=2? ,

where L is the length of the pendulum and g is the gravitational acceleration.

In order to increase the accuracy of the final result, the time of the oscillations must be measured several times. The average of these values will be taken as the time it takes for the pendulum to swing.

Preliminary Setup: Build a pendulum

• Cut a string approximately between 50cm and 80cm. Tie one end of the string to the bead and the other to the pencil.
• Tape the pencil onto a table or any other surface, so that the bead is hanging freely. This is your simple pendulum.

Activity: Determine the value of the gravitational acceleration.

Procedure: Determine the period of the oscillations.

1. Measure the length L of the string from the pencil end to the bead.
2. Pull the bead approximately 5 cm to the side from its equilibrium position and let it go.
3. Measure the time for 20 oscillations, t, and write it down.
4. Repeat the procedure seven times and in the table below record your data as t₁,   t_2,   t_3….
5. Average the seven values and report the average on the table as t_av.

1

6. Determine the period of oscillation by dividing the time t_av by 20. Report the value on the last column of the table.

Record your measurements in the following table:

L (m)	t1 (s)	t2 (s)	t3 (s)	t4 (s)	t5 (s)	t6 (s)	t7 (s)	tav (s)	Tav (s)

Results

Using the formula for the period of a simple pendulum, determine the gravitational acceleration, g. Write down the results in the following table:

L (m)	Tav (s)	g (m/s2)

Questions

1. How accurate is your result. Compare with the value for the gravitational acceleration. Fill the blank below.

Write the experimental value of the gravitational acceleration: ____________________

Write the established value of the gravitational acceleration: ______________________

The two values agree to which digit: _________________________________________

2. List all the factors (order them according to their impact) that might have affected the accuracy of your results.

3. Which of the above factors can be removed and which were outside your control?

Answer 1

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