Study Notes on Measuring Spring Constant in AP Physics 1

Introduction

  • Introduction to AP Physics 1, class number 1.8, focused on measuring a spring constant using various experimental methods.

  • Instructor: Greg Jacobs

  • Institution: Woodbury Forest School, a boarding school located in Central Virginia.

Spring Constant

  • Definition: A spring constant ($k$) is a property of a spring that indicates how stiff the spring is.

  • Concept Illustration:

    • Example with two springs: One is stiffer (higher spring constant) than the other, making it harder to pull.

Determining the Spring Constant Experimentally

Key Formula

  • The fundamental formula for determining the spring constant is:

    • F=kxF = kx

    • Where:

      • FF = force applied to the spring

      • kk = spring constant

      • xx = distance stretched from equilibrium or compressed position

Experimental Methods Overview

  • The presentation includes a playful game involving characters (Edna, Bertha, Anthony) to demonstrate different methods of measuring spring constants.

Anthony's Method (30 Minutes)

  • Setup: Anthony hangs a spring and applies varying weights to measure stretch.

  • Experiment:

    • Uses a mass to apply force to the spring.

    • Measures stretch with a ruler.

    • Observations:

    • 1.1 N applied force results in a stretch of some length (specific measurement not provided).

    • 2.0 N with a corresponding stretch observed.

    • Example Results:

    • 2.5 N = 12 cm stretch

    • 4.5 N = 22 cm stretch

  • Calculated Spring Constant:

    • k=0.20extextN/cmext(extor20extN/m)extextwithuncertaintyplusorminus0.01extN/cmk = 0.20 ext{ } ext{N/cm} ext{ }( ext{or } 20 ext{ N/m}) ext{ } ext{with uncertainty plus or minus } 0.01 ext{ N/cm}

Edna's Method (20 Minutes)

  • Setup: Edna holds the spring horizontally and uses a spring scale to apply force.

  • Experiment:

    • Measures original length of the spring (10 cm) and records force from the scale (0.8 N).

    • Continues measuring force and length to gather data.

  • Graphing Results:

    • Graphs force against length to find the slope of the line, which gives the spring constant.

    • Calculated Slope:

    • Found to be k=0.18extN/cmext(extor18extN/m)k = 0.18 ext{ N/cm} ext{ }( ext{or } 18 ext{ N/m})

    • Uncertainty or method detail not specified.

Anthony's Second Method (15 Minutes)

  • Setup: Anthony uses a digital force probe instead of hanging masses.

  • Experiment:

    • Pulls the spring with a force probe and measures stretching again with a ruler.

    • Records the force applied:

    • 1.1 N = 5 cm stretch

    • 2.0 N = 10 cm stretch

  • Calculated Spring Constant:

    • k=21extN/mextwithuncertaintyplusorminus1extN/mk = 21 ext{ N/m} ext{ with uncertainty plus or minus } 1 ext{ N/m}

Bertha's Method (10 Seconds)

  • Setup: Bertha uses advanced technology with a motion detector and a force probe.

  • Experiment:

    • The motion detector measures the position of the spring 20 times per second.

    • Data exported every 20 times per second to record force and position data for analysis.

  • Results:

    • Obtains a spring constant based on the slope of the graph created during the test.

    • Measured spring constant: k=18extN/mk = 18 ext{ N/m}

Conclusion

  • Summary of Methods:

    • Illustrated four distinct methods used to determine the spring constant with varying degrees of complexity and technology utilization.

  • Implication for Students:

    • Future exams may not ask for quick measurement methods but will likely require knowledge of experimental procedures to determine a spring constant effectively.

  • Final note from Greg Jacobs: Encouragement for students to design their measurement procedure for the spring constant.

  • Closing remarks: "Goodnight" from the instructor.