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Video Activity: Gravitational Field Strength and the Pendulum

We’ve been wanting to create a video set where students can vary the effective gravitational field strength to see how it affects the period of a pendulum and we’d come up with three methods:

  1. Travel to other planets, bringing a pendulum and camera.

  2. Attach a pendulum apparatus to a string and lower the apparatus with various vertical accelerations and, by Einstein’s Equivalence Principle, vary the effective gravitational field strength. For example, if we attached the pendulum apparatus to a very large Atwood’s machine, we could vary the combination of masses to change the vertical acceleration. This too seemed impractical due to the very large vertical distances over which the apparatus would need to fall in order to have enough time to measure the period of the pendulum.

  3. Create a pendulum that swings on a circular track. By varying the angle of the track, we could dilute the gravitational field, as Galileo did in his famous inclined-plane experiments. To reduce friction, we’d use a high-temperature superconductor cooled with liquid nitrogen levitated on a circular magnetic track.

We decided on #3. Here's the apparatus:

 A levitated puck swings nearly frictionlessly from a tilted circular track.

A levitated puck swings nearly frictionlessly from a tilted circular track.

Here’s the side view. From this perspective, students can use the video to measure the angle, and calculate the effective strength of the gravitational field.

 This is the side view student use in the activity. Using the interactive protractor, students measure the ramp angle and use it to calculate the effective gravitational field strength.

This is the side view student use in the activity. Using the interactive protractor, students measure the ramp angle and use it to calculate the effective gravitational field strength.

We recorded nine trials, each with a different tilt angle. In each case, we recorded a side view, for measuring the tilt angle, and a top-down view for measuring period.

We recently introduced new trig functions for making calculated columns, so the requisite functions for linearizing data are ready to go.

Here are two ways teachers can use this video set. Use it in the style of an AP Physics C question where students linearize a data set and use the slope to determine an unknown value. In this case, students can linearize Period vs Angle, and use the slope to determine the pendulum length.

Alternatively, do it as an in class activity as an example of applying the equation for the period of a simple pendulum. Have students select a trial, measure the period, solve for the effective gravitational field strength that causes a pendulum to swing with that period. Then have them measure the angle, calculate the effective gravitational field strength and compare those values. Make special note of trial 1, where the value of the effective gravitational field strength is a familiar value. Maybe this method was used to fake the moon landing (joking!)

Peter Bohacek