## Purpose

The purpose of this experiment is to determine the relationship between the vertical depression of the free end of a meter stick and the weight sticks attached.

## Theory

Hooke’s Law shows that when an elastic material is deformed, restoring forces will arise which try to bring the material back to its starting situation. The larger the distortion, the larger the resisting forces. Consequently, if there is more distorting forces then there will be a greater amount of distortion that occurs.

## Procedure

A meter stick was clamped horizontally, so that 80 cm of it projects beyond the lab table. The height from the free end of the meter stick to the floor was measured. Then, a 200 gram mass was attached to the free end of the meter stick. The vertical height from the free end of the floor was measured. After this, the vertical depression was determined. Finally, 200 gram amounts were continuously added to the free end of the meter stick until the total reached 1000 grams.

## Observations

As more weight was added to the free end of the meter stick, the further the meter stick bent.

## Data

The data recorded, related to the mass added to the end of the meter stick in grams (g), and the vertical height in centimetres(cm). The data for this is found in Table 1 at the back of the report.

**Table 1**

“Weight” attached, W(g) | Vertical Height, h (cm) |

0 | 94 |

200 | 91.5 |

400 | 89 |

600 | 86.5 |

800 | 84 |

1000 | 81.5 |

1200 | 79 |

**Table 2**

“Weight” attached, W(g) | Vertical Height, h (cm) | Vertical Depr, VD (cm) |

0 | 94 | 0 |

200 | 91.5 | 2.5 |

400 | 89 | 5 |

600 | 86.5 | 7.5 |

800 | 84 | 10 |

1000 | 81.5 | 12.5 |

1200 | 79 | 15 |

## Analysis

- The data from table 1 allowed for the vertical depression to be calculated.
- This occurred by subtracting the vertical height after the addition of each new weight, from the original vertical height.
- This data will be seen in Table 2 from above
- The data found in Graph 1 appears as linear. The vertical depression and the weight are proportional to each other.
- A proportionality statement which describes this relationship is VD proportional to W
- Therefore V=kW
- In order to find “k” in the equation the slope must be found (y2-y1)/(x2-x1)

## Discussion

This lab went fairly smoothly, with few problems. It was quite easy to find the proportionality between the vertical depression and the weight. While doing this lab the numbers which were found were generally simple. Most of the numbers were either whole, or had a decimal point of .5. The lab was also simple as it easily showed a linear equation once completed. One complication which occurred from this lab was the fact that it was done without the equipment to require good accuracy. It was difficult to find the vertical height past a tenth of a centimetre. Anything further than this would have been a pure guess. The other complication which may have occurred was where the weights were placed on the meter stick. If the weights had been hung to close to the table, then the weights would be completely different.

## Conclusion

In conclusion the relationship has been shown as the vertical depression being directly proportional to the weight or VD proportional to W. The constant has been shown as 0.0125 g/cm. The equation is seen as VD=(0.0125)W.

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