Free Falling Bodies - Lab Report Summary

Objectives

• Measure the acceleration of an object due to gravity.
• Compare the experimental value of $g$ to the theoretical value.

Materials and Equipment

• Meter stick
• Metal sphere
• Tennis ball
• Stopwatch

Theory

• Free-fall: Object's motion under gravity alone.
• Acceleration due to gravity ($g$) is approximately $9.8 m/s^2$.
• All objects in free fall experience the same acceleration regardless of mass (Galileo).

Procedures

• Assign fixed heights (e.g., 1.5 m, 2 m, 2.5 m).
• Record the time for the metal sphere to fall for three trials per height.
• Calculate the experimental $g$ using the formula: $g = \frac{2h}{t^2}$.
• Compute the percent error.
• Repeat steps with a tennis ball.

Calculations

• Calculate average time for each height.
• Calculate $g$ for each height using $g = \frac{2h}{t^2}$.
• Determine amount of error: $\text{Amount of Error} = |\text{Average } g - \text{True } g|$
• Calculate percentage error: $\text{Percentage Error} = \frac{{\text{Average } g - \text{True } g}}{{\text{True } g}} \times 100$

Questions

• Value of g vs Height: Variations in calculated $g$ values occurred with increased height due to inconsistent time measurements; accuracy and consistency are important.
• Factors Affecting Discrepancy: Air resistance, human error in timing, instrument limitations, object shape, and environmental changes.
• Effect of Altitude: Increased altitude slightly reduces $g$ due to the inverse square law, but it's negligible at typical heights.
• Free Fall Definition: Motion solely under gravity, with constant downward acceleration, differing from other motions due to the absence of other forces like air resistance.