PhysicsLAB: Calculation of "g" Using Two Types of Pendulums

In this lab you will be experimentally calculating the local value for the Earth's gravitational field strength using data collected from two types of pendula: a simple pendulum and a conical pendulum.

Refer to the following information for the next two questions.

Simple Pendulum: Data Collection

During each trial, multiple individuals in the class will simultaneously time 10 complete vibrations for the constant length pendulum that will be released at a small angular displacement (amplitude). The experiment will be repeated three times. In the table below, record the class average of timing information from each of the three trials.

Length of pendulum (m)

mass of bob (kg)

trial	average of class times for 10 vib	time for one vibration
	(seconds)	(seconds)

Refer to the following information for the next three questions.

Analysis of Data

Was there a reasonable agreement between the final average experimental periods from each of the three trials?

yesno

Did you consider any of the final experimental values from any of the three trials to be an outlier? Explain why.

Determine the BEST average experimental period for you pendulum based on the previous two answers. Express your answer in seconds.

Refer to the following information for the next question.

Conclusion (Part I)

Show below is the accepted formula for the period of a simple pendulum.

State your class value for the local value of gravity based on timing a simple pendulum.

Refer to the following information for the next question.

Conical Pendulum: Data Collection

When viewed from above, the path taken by a conical pendulum is a horizontal circle. A freebody diagram of the forces acting on the pendulum's bob and the resolution of those forces are also shown.

Begin by tracing out a circle on the floor of the classroom. In my room we use pieces of tape to mark the circumference of the circle. Use the same length string and pendulum bob mass from the previous experimentation on a simple pendulum. For logistics, I suggest that the length of the pendulum be no less than twice the radius of the circle.

After practicing to keep the "bob on track," the class will once again, simultaneously time 10 complete revolutions for the constant radius conical pendulum. This experiment will be repeated three times. You will record the class average of timing information from each of the three trials.

radius of circle (m)

trial	average of class times for 10 revs	time for one revolution
	(seconds)	(seconds)

Refer to the following information for the next three questions.

Analysis of Data

Was there a reasonable agreement between the final experimental period from each of the three trials?

yesno

Did you consider any of the final experimental values from any of the three trials to be an outlier? Explain why.

Determine the BEST average experimental period for you conical pendulum based on the previous two answers.

Refer to the following information for the next five questions.

Conclusion (Part II)

Show below are the equations for a conical pendulum. The "T's" in equations #1 and #2 represent the tension in the string.

(#1) T cosθ = mg

(#2) T sinθ = F_C = mv²/r

You calculate theta by using sin theta = r/L
You can calculate velocity by using v = 2πr/T_period
Knowing the mass of the bob you can calculate the tension (equation #2).
Knowing the tension you can then calculate the gravitational field strength (Equation #1).

What was the angle (in degrees) for your conical pendulum trials?

What was the magnitude of the average tangential velocity of the conical pendulum's bob?

What was the average tension in the string while data was being taken on the conical pendulum?

What the tension greater than, equal to, or less than the weight of the bob?

greater thanequal toless than

State your class value for the local value of gravity based on timing a conical pendulum of constant radius, length, and mass.

Error Discussion

Calculate a percent difference between your two class values for "g."

Which method of obtaining "g" do you feel was the most precise? That is, replicable.

simple pendulumconical pendulum

Support your pervious choice.