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Understanding Energy Conservation and Dimensional Analysis in Behavioral Units

Explore the principles of energy conservation in kinetic and potential forms, alongside dimensional analysis in behavioral units. Discover the constants of motion and the role of dimensional consistency in related calculations.

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Understanding Energy Conservation and Dimensional Analysis in Behavioral Units

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  1. DIMENSION IN ACTIONANDTHE PROBLEM OF BEHAVIORAL UNITSM. Jackson Marrmm27@prism.gatech.edu

  2. KINETIC ENERGY = 1/2 m v2 = M L2/T2 POTENTIAL ENERGY = m g h = M L2/T2 TOTAL ENERGY = K + P (conserved) TOTAL ENERGY IS A CONSTANT OF MOTION

  3. DIMENSIONAL CONSISTENCY? B = k r / (r + ro) Rout = {ln [1+(PB/γPR)(exp [1/Rin] – 1]} -1

  4. log [cabin] = ?! But, log [4 cabins / 2 cabins] = log 2 = 0.30103.

  5. Dimensional Analysis Period of a Pendulum T= f (L, g, m)? T1 = La (L T-2)b Mc in units of length, mass, and time. Solve for a, b, and c to yield dimensional consistency. a =1/2, b = -1/2, c =0, gives: T = k (L/g)1/2 , where k is dimensionless. In fact, k = 2π.

  6. Allometry in Birds

  7. If f (x) = c xα then, log f (x) = log c + α log x. This is a linear function on a log-log-scale.

  8. Scaling in IRT>t Schedules IRT>t Scheduled Value

  9. Scaling Rate and Response Number in FI Schedules

  10. Scale Invariance in FI Schedules with  = 1

  11. Rate-Dependency In FI Schedules (CPZ) Control Rate

  12. Skill Performance with Practice (Anderson, 2000)

  13. Baum’s Law (B1 / B2) = b(r1 / r2)a b: bias a: sensitivity

  14. 1/f noise in IRT>t schedules?

  15. FI 10 (FR 20: Sp)

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