# 062 Laboratory Six: Gram force extension of an elastic band

## Goal

Determine the mathematical relationship between force and the lengthening of an elastic band. Hooke's law for steel springs states that Force f = k × distance d where k is a constant called Hooke's constant. Materials that obey this relationship are called Hookean materials.

In this laboratory distances will be measured using centimeters. The force will be measured using grams of mass. When grams are used to express force, the force is called a gram-force. One gram-force is the force exerted by a one gram mass at rest on the surface of the planet earth.

## Equipment

• stryrofoam cups
• yarn
• elastic bands
• marbles

## Procedure

1. Attach a cup to a string comprised of lengths of yarn and a single length of elastic band.
2. Suspend the cup from the ceiling or a hook on the overhead track.
3. Adjust the height of the empty cup so that the cup is one meter above a table.
4. Measure the mass m of a marble in grams and then add the marble to the cup.
5. Measure the extension distance d in centimeters.
6. Repeat the above two steps, massing and adding marbles one at a time until you have added 30 marbles. With each additional marble, measure the extension of the elastic band.

Note that the force is technically called a "gram-force." Mass is not force, a gram-force is the force exerted by one gram as a result of the acceleration of gravity.

## Data tables [d] [t]

Design an appropriate table with the extension distance d (centimeters) as the independent variable [x axis] and the gram-force of the marbles m (grams) versus the as the dependent variable [y axis].

## Graph [g]

Use the appropriate graph type in order to run an analysis of the mathematical relationship for this system.

## Analysis [a]

Based on the mathematical relationship, report the appropriate values in your analysis.

## Conclusions [c]

Wrap up with a discussion appropriate to this laboratory. Discuss whether the system is "predictable," that is, if given a mass m could one make reliable predictions of distance d? Do some background research on Hooke's law of elasticity. In the conclusion, discuss whether the elastic band is a linear elastic ("Hookean") material.