# The gravitational attractive force of the English Dept.

Bill Witte
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#### Summary

By measuring the gravitational force in the basement and on the roof of the Gruening Bldg. students will determine the gravitational attraction of the building and its contents and estimate the mass of the building.

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## Context

#### Audience

As we have taught it, this lab is embedded in an introductory geology class for majors. We have also used it as an intro to a field geophysics lab on gravity.
Integrates geophysics into a core course in geology
Designed for an introductory geology course

#### Skills and concepts that students must have mastered

Before they start, students must be familiar with the gravitational equation, the definitions of mass and force, and the variation of gravity with elevation. They must be capable of measuring distances with a tape measure and will be taught to level and read a simple (Worden) gravimeter.

#### How the activity is situated in the course

We use it as an introductory homework or lab exercise to introduce gravity prior to discussing the Earth's magnetic field.

## Goals

#### Content/concepts goals for this activity

1)Measuring the gravitational force at two points, comparing the observed difference from that predicted by the free-air correction. 2)Using the discrepancy between the prediction and observation, estimate the mass of the building.

#### Higher order thinking skills goals for this activity

1)Visualize the gravitational force as a vector (not always "down"), 2)Prediction testing, analyzing and exploring a discrepancy, 3)Development of more complicated models to explain a discrepancy.

#### Other skills goals for this activity

Qualitative experience of different noise environments - it's harder to make a measurement on the 6th floor next to the elevator. Careful measurement techniques with electromechanical instruments.

## Description of the activity/assignment

This exercise starts with homework readings an instructor-lead discussion of the Earth's gravity and the gravitational force ending with a free-air gravity formula. The students are then introduced to operation of the Worden gravimeter and, in pairs, measure the gravity difference between a site on the ground floor and on the roof. They pool their data and determine their best estimate of the difference - which they compare to the free-air prediction. Typically the observation and prediction disagree, and the students are asked to formulate hypotheses for the difference. The gravitational force due to the building and contents is an easy hypothesis to test using the gravity formula and leads to an estimate of the mass of the building. The students compare this to simple estimates of the mass of the building (6 concrete slabs, 20m x 20m x .3m x the density of concrete) using measurements the students make and densities available in references.

Uses online and/or real-time data
Has minimal/no quantitative component

## Determining whether students have met the goals

Can the students draw a picture that shows the forces acting on the two measurement sites? Can the students calculate the discrepancy between the observed force and the predicted free-air difference? Can the students calculate the size of the mass that would explain the discrepancy? Can the students walk through the building and estimate the total mass of the building making realistic simplifying assumptions? 