Hooke's Law Investigation — a Plot45 Write report

Hooke’s Law Investigation

Aim

To investigate how the extension of a spring changes as the mass hanging from it increases, and to determine the spring constant.

Hypothesis

The extension of the spring will be directly proportional to the applied force, provided that the elastic limit is not exceeded.

Apparatus

Retort stand, boss and rod
Spring
1m ruler
Mass hanger and slotted masses

Method

The spring was suspended from a retort stand beside a ruler. Its initial length was recorded. Masses were added in 10 g intervals from 0 g to 100 g. The new length was measured each time, and the extension was calculated.

Results

As the mass increased, the extension of the spring also increased. The graph of extension against mass produced an approximately straight line.

Best-fit equation:

e = 0.0631 m + 0.135

where $e$ is the extension in centimetres and $m$ is the mass in grams.

Analysis

The gradient of the graph was:

0.0631 c m g^{- 1} = 0.631 m k g^{- 1}

Since

F = k x

and $F = m g$ ,

k = \frac{g}{g r a d i e n t}

k = \frac{9.81}{0.631} \approx 15.5 N m^{- 1}

Conclusion

The extension was approximately proportional to the applied force, supporting Hooke’s law. The experimental spring constant was approximately:

k = 15.5 N m^{- 1}

Evaluation

Small differences from the expected value may have been caused by uncertainty when reading the ruler or movement of the spring. Using a pointer and waiting for the spring to stop oscillating would improve the measurements.