phys_230_lab_06-1

Lab 6: Centripetal Force

1. Introduction

• Definition of Centripetal Force:

  • Coined by Isaac Newton as vis centripeta meaning "seeking the center" in Latin.

  • Initially introduced while studying planetary motion, later applicable to any circular motion.

2. Equipment

• Required apparatus include:

  • Centripetal force apparatus ME-8951

  • Wireless force sensor PS-3202

  • Universal Interface UI-5000

  • Power supply

  • Electric motor

  • Spirit level

3. General Setup

3.1 Description

• The apparatus consists of:

  • A base, rotating platform, and motor.

  • The platform can rotate freely; speed can be adjusted.

• Adjusting speed allows investigation of effects on centripetal force.

• The force sensor measures both force and angular velocity via a built-in gyroscope.

3.2 Preparing to Measure

• Steps for setup:

  • Attach the wireless force sensor to the rotating platform.

  • Align the vertical rod with the rotating axis.

  • Ensure the platform is level using a spirit level.

3.3 Power Supply

• Using an electric motor:

  • Connect motor to power supply.

  • Adjust voltage to control motor speed (2-4 V for moderate rates).

  • Ensure safety when handling the power supply while turned on.

4. Theory

• Centripetal Force Equation:

  • Fc = m * ac

    • Where Fc = centripetal force, m = mass of spinning object, ac = centripetal acceleration.

• Centripetal Acceleration Formula:

  • ac = v²/R

    • Where v = linear speed, R = radius of rotation.

• Relation Between Linear and Angular Speed:

  • v = ωR

    • Where ω = angular speed.

• Derived Equations:

  • ac can also be expressed as: ac = ω²R.

  • Final form for centripetal force: Fc = mω²R.

5. Setup A: Dependence on Angular Velocity

5.1 Procedures

• Keep mass (20g) and radius (20cm) constant:

  • Ensure the mass coincides with the 20 cm mark.

  • Record initial force (Fc) and angular velocity (ω) after adjusting motor voltage to about 5 V.

  • Increase voltage by 0.5 V increments, recording Fc and ω until 11 V is reached.

5.2 Analysis

• Square ω values for data.

• Perform linear fit of Fc vs. ω²:

  • Fc = Aω², slope A = mR.

  • Calculate theoretical mass (m) from slope A.

6. Setup B: Dependence on Radius

6.1 Procedures

• Keep mass and angular velocity constant (same 20g mass):

  • Start at 10 cm radius, adjusting to 25 rad/s.

  • Move mass incrementally (1cm) up to 24 cm, recording force.

6.2 Analysis

• Perform linear fit of Fc vs. R:

  • Theoretical slope B = mω².

  • Calculate mass (m) from slope B.

7. Setup C: Dependence on Mass

7.1 Procedures

• Keep radius (20cm) and angular velocity constant (25 rad/s):

  • Select masses from 5g to 50g.

  • Record force for each mass while ensuring angular speed around 25 rad/s.

7.2 Analysis

• Conduct linear fit of Fc vs. m:

  • Slope C = ω²R.

  • Calculate radius (R) from slope C and compare with measured radius.