Understanding Percentage Error
Percentage error tells you how much your measured value deviates from the accepted (or theoretical) value, expressed as a percentage.
Formula:
```
Percentage Error = [(|Measured Value - Accepted Value|) / Accepted Value] * 100%
```
Applying it to Acceleration Due to Gravity
1. Measured Value: This is the value you obtain from your experiment (e.g., using a pendulum, free-fall apparatus, etc.).
2. Accepted Value: This is the standard or theoretical value of acceleration due to gravity (approximately 9.81 m/s² at sea level).
Example:
Let's say you measure the acceleration due to gravity to be 9.65 m/s². Here's how you would calculate the percentage error:
* Measured Value: 9.65 m/s²
* Accepted Value: 9.81 m/s²
Calculation:
```
Percentage Error = [(|9.65 - 9.81|) / 9.81] * 100%
= (0.16 / 9.81) * 100%
≈ 1.63%
```
Key Considerations:
* Units: Make sure your measured and accepted values use the same units (in this case, meters per second squared).
* Significant Figures: Round your percentage error to the appropriate number of significant figures, which is usually determined by the least precise measurement in your experiment.
* Sources of Error: Understand the potential sources of error in your experiment. These could include:
* Measurement uncertainties in your apparatus
* Air resistance
* Friction
* Variations in the local gravitational field
Interpreting the Result:
The percentage error gives you an idea of how accurate your experiment was. A smaller percentage error indicates a more accurate result.
Let me know if you have any more questions about specific experimental setups or calculations!
