← The Thinking Experiment 📐 Physics Lab Activity

Measuring “g” on Earth’s Surface: Photogates & Ticker Tape Lab

Determine the acceleration due to gravity on Earth by comparing two classic experimental methods: 4 dual-beam digital photogates and a 60 Hz ticker tape timer with quadratic curve fitting.

Standard: g = 9.80 m/s²

1. Laboratory Setup & Pedagogical Guide

Learn the principles of dual-sensor photogates and 60 Hz ticker timers, identify equipment components, and understand how data is collected.

🔬 Laboratory Equipment & Apparatus Orientation

100 80 60 40 20 Photogate 1 (Gate 1 & Gate 2) y₁ = 0.800 m, y₂ = 0.780 m (Δ=2cm) Photogate 2 (Gate 1 & Gate 2) y₁ = 0.600 m, y₂ = 0.580 m (Δ=2cm) Photogate 3 (Gate 1 & Gate 2) y₁ = 0.400 m, y₂ = 0.380 m (Δ=2cm) Photogate 4 (Gate 1 & Gate 2) y₁ = 0.200 m, y₂ = 0.180 m (Δ=2cm) Falling Cylinder
Dual-Sensor Photogate Principles Each modern digital photogate unit contains two internal optical sensors (Gate 1 at the top and Gate 2 at the bottom, spaced exactly 2.0 cm apart). Across 4 photogates, students collect 8 distinct position and time data points!

Experimental Protocol

  1. Measure Gate Heights: Always align your eye level with the small optical hole of each sensor. Measure both Gate 1 and Gate 2.
  2. Record Block Times: When the falling cylinder cuts through the light beam, the digital sensor state transitions from 0 to 1. Record this exact timestamp.
  3. Watch for Sensor Shuffling: In digital setups, wireless sensors can occasionally report channels out of physical vertical order. Always match the channel ID to its measured height!
Measurement Best Practices
  • Height Measurement: Align the ruler's horizontal sightline directly with the sensor beam aperture before recording each height.
  • Release Technique: Support the cylinder gently right above the first gate and release smoothly from rest.
  • Data Verification: Compare the recorded timestamps with the physical gate order on the stand.

⏱️ Photogate Drop Stand

4 Units · 8 Sensors
Height: 0.800 m (80.0 cm)
Cursor:
📍 Release Height (y_drop): m
Δy = 0.0 cm (flush at Gate 1)
🔧 Move Photogates (Gate 1 Height): (Drag on stand or enter heights below)

📡 Digital Sensor Event Log

Time (s) Sensor Unit Channel State
Ready. Click "Drop Object" to capture photogate block timestamps.

📋 Student Data Table (Method I)

Sensor Gate Height y (m) Time t (s) [State = 1]

📜 60 Hz Ticker Tape Drop Apparatus

Frequency: 60 Hz (Δt = 1/60 s ≈ 0.01667 s) The clapper strikes 60 times per second. Spacing expands quadratically with constant acceleration.

📐 Tape Inspection & Ruler Workbench

💡 Click any dot to set as Dot 0. Drag the yellow ruler to measure 12 points.
⚪ Fresh Blank Strip Loaded Active Dot 0: #—
Zoom: 1.0x
12 Points at Δt = 0.0167 s each

📋 Student Data Table (Method II)

Dot # Time t (s) [n/60] Position y (m)

📈 Position vs. Time & Quadratic Fit

Quadratic Fit Parameters

Model Assumptions & Theory
Empirical fit: y = At² + Bt + C. Standard parabolic freefall model with initial velocity and position parameters.

📝 Official Student Lab Handout Document

Lab: Measuring the Acceleration Due to Gravity on Earth’s Surface “g”

Purpose

In this lab we are going to find out the value of the acceleration of gravity on Earth, “g”, by two methods.

Method I: Photogates

  1. Using the photogates, create a Position vs. Time graph.
  2. Apply a quadratic fit for the parabola.
  3. Copy and paste the graph below

[Method I: Photogates Position vs. Time Graph]

Plot your photogates data in the Analysis tab, or click below to attach the graph:

Method II: Ticker Tape

  1. Using the values of the points in the ticker tape, create a Position vs. Time graph.
  2. Apply a quadratic fit for the parabola.
  3. Copy and paste the graph below

[Method II: Ticker Tape Position vs. Time Graph]

Plot your ticker tape data in the Analysis tab, or click below to attach the graph:

Analysis of the Data

1. In the table below, write the initial position, initial velocity, and acceleration for each case according to the quadratic fit equation.

Photogates Ticker Tape
y₀ =
v₀ᵧ =
a =
g =
y₀ =
v₀ᵧ =
a =
g =

2. Calculate the % difference in each case by comparing with the reference value of g = 9.8 m/s².

Photogates Ticker Tape
% diff = |(Experimental - Reference) / Reference| * 100%
% diff = (|____ - 9.8| / 9.8) * 100%
% difference =
% diff = |(Experimental - Reference) / Reference| * 100%
% diff = (|____ - 9.8| / 9.8) * 100%
% difference =

3. Explain why your measured values might differ from the reference value. Mention only reasons that would actually affect the value in a significant way. Write at least 3 valid reasons.

4. Alternative Analysis: Linearization (y versus t²)

Inquiry Extension

Assume the simplified freefall relationship where v0y = 0: y = ½at² + y₀. Graphing y versus t² yields a linear model: y = M·(t²) + K, where the slope represents M = ½a (hence a = 2·M and g = 2·|M|).

Photogates Linearized (y vs. t²) Ticker Tape Linearized (y vs. t²)
Slope (M) =
Intercept (K) =
g = 2·|M| =
Slope (M) =
Intercept (K) =
g = 2·|M| =