# Centripetal Force vs Radial Acceleration Graph ## Instructions 1. Use Excel or similar software. 2. Input your data from Table. 3. Plot **Centretal Force (N)** on the y-axis. 4. Plot **Radial Acceleration (m/s²)** on the x-axis. 5. Generate the graph and analyze the slope. --- ## Example Data (Hypothetical for illustration) | Radial Acceleration (m/s²) | Centripetal Force (N) | |----------------------------|-----------------------| | 2 | .5 | | 4 | 1. | | 6 | 1.5 | | 8 | 2. | | 10 | 2.5 | --- ## Plot Description - The graph should show a **linear relationship**. - The slope represents the proportionality constant between force and acceleration. --- ## Slope Calculation - In Excel, you can find the slope using the `=SLOPE(known_y's, known_x's)` function. - Based on the example data, the slope would be approximately: \[ \text{Slope} \approx \frac{\Delta \text{Force}}{\Delta \text{Acceleration}} \approx \frac{2.5 - .5}{10 - 2} = \frac{2.}{8} = .25 \, \text{N·s}^2/\text{m} \] ## Expected Value - The theoretical relation is: \[ F_c = m \times a \] - Where: - \(F_c\) = centripetal force - \(m\) = mass (kg) - \(a\) = radial acceleration (m/s²) - The slope should match the mass \(m\) used in the experiment if the data aligns perfectly. --- ## Summary - **Determine the slope** from your graph. - **Compare** it with the expected mass. - **Check for consistency** to validate your experimental data.