phys_230_lab_07

Lab 7: Launching Tube

1. Introduction

  • Objective: Test the Law of Conservation of Energy with a Launching Tube apparatus.

  • Historical Background:

    • Proposed by Emilie du Châtelet (1706-1749).

      • Studied balls dropped onto soft clay, observing the size of holes created was proportional to both the initial height and the square of impact velocity.

    • Explored further by James Prescott Joule (1818-1889).

      • Found that mechanical energy converts to thermal energy.

  • Key Principle: Conservation of mechanical energy involves both kinetic and potential energies.

2. Equipment

  • Photogate System: ME-9498A PASPORT Digital Adapter (PS-2159, UI-5000).

  • Launching Tube Apparatus: Includes a metal ball, plumb bob, catcher box, and a meter stick.

3. General Setup

3.1 Description

  • Detailed Setup of Launching Tube:

    • Curved pipe mounted on a frame, adjust tilt with screws.

    • Release lever at the long side; short side has two photogates.

  • Adjustments: Tilt to vary initial and final heights; affects whether the ball flies off or rolls back.

3.1.1 Goal of the Experiment

  • Use conservation of energy to predict the ball's speed as it exits the tube.

  • Measure the actual speed with photogates and compare theoretical vs experimental speeds.

3.2 Preparing to Measure

  • Speed Measurement Preparation:

    • Attach photogates to the tube, making sure they align vertically and the beam is unobstructed.

    • Connect photogates to the Digital Adapter.

    • Ensure photogate positioning is correct for optimal performance.

4. Setup A: Estimating Friction

4.1 Experimental Setup

  • Friction Observation: Noted by sound; energy is lost as sound, heat, and vibrations.

  • Trial and Error Method: Adjust the tilt of the tube until the ball does not exit when released; measure initial (hA0) and final (hAf) heights accurately with plumb bob and meter stick.

4.2 Setup A Calculations

  • Energy Dissipation:

    • The energy change is represented as: ∆E = WFf

    • WFf: work done by friction = -FE (energy lost to friction).

  • Mechanical Energy Equation:

    • E = K + U, where K = kinetic energy, U = gravitational potential energy.

  • Potential Energy Formula:

    • U = mgh, where m = mass (kg), g = gravitational acceleration (9.81 m/s²), h = height (m).

  • Final Energy Loss Equation:

    • F_E = mg(hA0 - hAf).

5. Setup B: Launching the Ball

5.1 Experimental Setup

  • Launching Procedure: Lower the short side for the ball to land about 1 meter away.

  • Record Measurements: Repeat the launch at least six times; collect exit speeds to calculate average.

5.2 Setup B Calculations

  • Energy Change Equation:

    • Apply conservation principles: ∆E = WFf.

  • Kinetic Energy Components:

    • Translational: K_T = (1/2)mv²

    • Rotational: K_R = (2/5)mv²

    • Total: K = K_T + K_R = (7/10)mv² when ball leaves the tube.

  • Final Speed Equation:

    • Speed of ball can be calculated using: v = r * sqrt[10/7 * g(hB0 - hBf - hA0 + hAf)].

Conclusion

  • Discuss how to compute and compare theoretical speed with experimental results in the lab report.