# Given a Batch of Factory Springs, Estimate the Average Spring Constant and Uncertainty of the Batch.

Given a Batch of Factory Springs, Estimate the Average Spring Constant and Uncertainty of the Batch.

## Outline plan

I have been given 3 springs to which I will add different weight. Using the value of extension (Δx) I will calculate the spring constant. Hooke's Law says that the stretch of a spring from its rest position is linearly proportional to the applied force (stress is proportional to strain). Symbolically,

F = kΔx

Where F stands for the applied force, x is the amount of stretch (found by new length minus original length), and k is a constant that depends on the "stiffness" of the spring, called the spring constant.

## Trial plan

Set up equipment as above. Measure original length of spring. Add weights 0.5N at a time until spring reaches elastic limit. Record extension (Δx). Plot these results on a graph and use this information to gain a sensible number and range of values to use in full experiment.

Safety Notes

Be sure to keep your feet out of the area in which the masses will fall if the spring breaks
Be sure to clamp the stand to the lab table, or weight it with several books so that the mass does not pull it off the table.
You need to hang enough mass to the end of the spring to get a measurable stretch, but
too much force will permanently damage the spring, as it will have exceeded its elastic limit.

Wear safety glasses to protect eyes if spring suddenly recoils.

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## Apparatus list

1 Stand

1 Clamp

1 Boss

1 hanger

3 provided springs

0 – 100.0cm ruler

1 paper clip

Set of known masses

## Detailed plan

Assemble the apparatus as shown in the diagram above. Be sure to clamp the stand to the lab table, or weight it with several books. Some springs tend to be "clenched" - their coils are pressing against each other, and it takes a small force to simply get the spring to the point that it will begin to stretch. If this is the case, I will hang a small mass (20 g – 50 g) from the spring initially and consider that to be the spring’s starting position. Making a small pointer out of a bent paper clip and fixing it to the end of the spring acts well to indicate clearly the position of the spring in relation to the ruler.

The data that I will need to record are the rest position of the spring (same for each trial), stretched position of the spring, and the total mass hanging from the spring for each weight added.  I will check the weights of the loads on electronic scales to ensure they are correct.

I will add the weights in 1 N loads, starting with 2N, and record the extension (Δx) in cm. I will do this until 10 N have been added. I will then repeat this twice for each of the three springs. I will repeat this using ...