Introduction to Projectile Motion Lab¶

Welcome to the Projectile Motion Laboratory! In this experiment, we will analyze the motion of a projectile launched at different angles and initial velocities. Projectile motion is a key topic in kinematics, describing the curved path of an object under the influence of gravity when launched into the air. By conducting controlled experiments, we will compare theoretical predictions with real-world measurements.

The motion of a projectile can be broken down into two independent components:

Horizontal motion: Constant velocity, since no horizontal forces act on the projectile (assuming air resistance is negligible).
Vertical motion: Constant acceleration due to gravity ($ g = 9.81 \text{ m/s}^2 $), influencing the projectile’s height and time of flight.

Using the kinematic equations, the horizontal range of a projectile launched at an angle $ \theta $ with initial velocity $ v_0 $ is given by:

$R = \frac{v_0^2 \sin 2\theta}{g}$

For launches from a height $ y_0 $, a more detailed equation accounts for the extra time the projectile spends in the air.

What You Will Learn¶

By the end of this lab, you will be able to:

Understand the principles of projectile motion and the effect of gravity.
Measure and analyze projectile motion using a dual-beam photogate and carbon paper.
Investigate how initial velocity and launch angle affect projectile range.
Compare experimental data with theoretical predictions, considering measurement uncertainties.
Discuss the impact of systematic and random errors in projectile motion experiments.

Overview of the Experiments¶

This lab consists of two main experiments:

Experiment 1: Horizontal Launch – Measuring Initial Velocity and Range¶

Launch a steel ball horizontally from a fixed height.
Measure the projectile’s initial velocity using a dual-beam photogate.
Determine the horizontal range and compare it with theoretical calculations.

Experiment 2: Angled Launch – Range vs. Launch Angle¶

Launch the projectile at various angles (e.g., 35°, 40°, 45°, 50°, and 55°).
Measure the range and initial velocity at each angle.
Compare experimental data with the theoretical model to determine the optimal launch angle for maximum range.

Equipment You Will Be Using¶

Projectile Launcher – Fires the steel ball at adjustable angles.
Dual-Beam Photogate – Measures the initial velocity of the projectile.
Steel Balls – Act as the projectiles.
Protractor – Measures the launch angle of the projectile.
Measuring Tape or Ruler – Determines the horizontal range.
Carbon Paper – Marks the projectile’s landing position for accurate measurement.
C-Clamp – Secures the launcher to the table.
Plumb Bob – Helps align measurements with a vertical reference.
Paper Tape – Provides a clear landing surface for range measurement.
Safety Glasses – Protects against accidental impacts.

Important Tips for Success¶

Calibrate Carefully: Use a level and plumb bob to ensure accurate launch angles and alignments.
Consistent Launch Conditions: Use the same launcher settings (spring tension) for all trials.
Precise Measurements: Record multiple trials and calculate averages to reduce random errors.
Error Analysis: Consider uncertainties in velocity, angle, and range when comparing data to theoretical predictions.