Table of Contents
Experiment Purpose
The projectile motion experiment is a cornerstone of introductory physics laboratory courses. Its goal is to verify the kinematic equations of projectile motion by launching a small ball (or other projectile) at a known velocity and angle, then measuring where it lands. By comparing the measured landing position with the theoretical prediction, students can evaluate the accuracy of the idealized model and identify sources of experimental error.
This calculator automates the comparison step. You enter the launch parameters (velocity, angle, height) and the measured range from your experiment. The calculator computes the theoretical range using the kinematic equations, then calculates the percent error between theory and measurement. A low percent error (under 5%) typically indicates good experimental technique and validates the projectile motion model under the test conditions.
Theoretical Background
The theoretical range accounts for the initial height h0 above the landing surface. When h0 = 0, this simplifies to the standard range formula. The percent error uses the theoretical value as the accepted (reference) value, following standard laboratory conventions. An error under 5% is generally considered acceptable for introductory physics labs.
Understanding Percent Error
| % Error Range | Assessment | Likely Cause |
|---|---|---|
| 0 - 2% | Excellent | Minor measurement uncertainty |
| 2 - 5% | Good | Typical random errors |
| 5 - 10% | Fair | Air resistance or measurement issues |
| 10 - 20% | Poor | Significant systematic errors |
| > 20% | Check setup | Equipment malfunction or incorrect parameters |
Common Error Sources
- Velocity measurement: If using a photogate or speed sensor, calibration errors directly affect the theoretical range. Even a 5% error in velocity produces a 10% error in range (since range scales as v²).
- Angle measurement: Protractor precision is typically limited to 1-2 degrees. Near 45 degrees, a 2-degree error changes the range by about 0.3%.
- Air resistance: Always reduces the actual range below theoretical. More significant for lightweight balls, high velocities, and large surface areas.
- Spin effects: If the projectile spins, the Magnus force can curve the trajectory sideways or alter the range.
- Landing detection: Carbon paper marks may spread, and bounce or roll after landing introduces systematic error.
Frequently Asked Questions
Why is my measured range always less than theoretical?
This is expected because the theoretical model ignores air resistance. Air drag always opposes motion and removes kinetic energy, resulting in a shorter actual range. The difference is larger at higher speeds and for lighter or larger projectiles. If your measured range is consistently greater than theoretical, check your velocity measurement device calibration.
How many trials should I run?
Standard practice is to run at least 5 trials for each set of conditions. Calculate the mean and standard deviation of your measured range. The standard deviation quantifies the random error in your measurements. Using the mean of multiple trials reduces the effect of random error by a factor of 1/sqrt(n), where n is the number of trials.
Should I use absolute or relative percent error?
Use percent error (relative to the theoretical value) for comparing theory to experiment. This normalizes the error by the expected value, making it meaningful across different magnitudes. A 1 cm error is significant for a 10 cm range (10%) but trivial for a 10 m range (0.1%). Always report whether you used the theoretical or measured value as the reference.