052 Laboratory Five: Gram force extension of an elastic band

16 September 2010

Question

Is there a linear relationship between the extension of an elastic band and force on the elastic band?

Goal

Explore 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 F, the force F 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

Instructional note: If one has no mass balances, simply consider the average mass of a duck marble to be five grams. The error that this will introduce will be small, essentially a linear transformation, and is tolerable in terms of the intent of this laboratory.

Procedure

1. Form teams of three people. One will hold the meter stick, steady the cup, and read the downward displacement. The secone will add marbles to the cup. The third will record data.
2. Attach a cup to a string comprised of lengths of yarn and a single length of elastic band.
3. Suspend the cup from the ceiling or a hook on the overhead track.
4. Adjust the height of the empty cup so that the cup is one meter above a table.
   
5. Measure the mass of an empty cup.
6. Measure the mass of all thirty marbles plus the cup.
7. Subtract the mass of the cup.
8. Divide by thirty and round to the nearest 0.1 g. Use the result as the mass per marble for each and every marble.
9. Add a marble to the cup.
10. Measure the extension distance d in centimeters.
    
11. Repeat the above two steps 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" (gmf). Mass is not force, a gram-force is the force exerted by one gram as a result of the acceleration of gravity (980 cm/s²).

Data tables [d] [t]

Graph [g]

Make an xy scattergraph of the data.

Analysis [a]

1. Is the relationship linear?
2. Comment on the nature of the graph.
3. If not, are sections of the graph "reasonably linear"?
4. Report the slope and intercept.

Conclusions [c]

Wrap up with a discussion appropriate to this laboratory. Discuss whether the system is "predictable," that is, if given a gram-force F could one make reliable predictions of distance d? Do some background research on Hooke's law of elasticity. Look it up on the Internet such as in the Wikipedia. In the conclusion, discuss whether the elastic band is a linear elastic ("Hookean") material.