20121222

Physics final exam problem: wind turbine rotational speeds

Physics 205A Final Exam, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 8.5

"Presentacion aerogenerador monopala pendular ADES"
1dezgz
http://youtu.be/f4JXRPAFvZI

"Enercon wind energy turbines in action"
HD1080ide
http://youtu.be/z6pEQevflmk

An ADES pendular wind turbine(*) consists of a long blade (mass 3,950 kg, length 18 m) and a shorter counterbalance blade (mass 5,800 kg, length 6 m). An ENERCON E-33 wind turbine(**) consists of three identical blades (each mass 1,900 kg, length 16 m). Treat all blades as beams of uniform thickness and density. Assuming that both wind turbines have approximately the same rotational kinetic energy while generating electricity, which turbine has a faster rate of rotation? Neglect drag. Show your work and explain your reasoning.

(*) Rated power 335 kW, rotor height [diameter] 36 m, 3,950 kg; pendulum 5,800 kg (pendulum arm length estimated from scale drawing)," http://www.ades.tv/en/products/pendular-wind-turbine/technical-data/id/242.
(**) "Nominal power 330 kW, blade length 15.6 m, rotor including hub/main pin 5.7 t," http://planning.northwarks.gov.uk/portal/servlets/AttachmentShowServlet?ImageName=233324.

Solution and grading rubric:
  • p = 20/20:
    Correct. Determines (a) rotational inertia of each wind turbine by summing the individual rotational inertiae of each component blade, and (b) equates rotational kinetic energies, such that the wind turbine with the smaller rotational inertia must have the faster rotation rate. (May have neglected to square rotational speed in expression for rotational kinetic energy in (b), either due to confounding rotational kinetic energy with angular momentum, or careless algebra.)
  • r = 16/20:
    Nearly correct, but includes minor math errors. One of (a) or (b) is correct, other part is substantive and nearly complete.
  • t = 12/20:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Substantive but problematic efforts in both (a) and (b); or one of (a) or (b) is nearly correct, but other is missing or insubstantive.
  • v = 8/20:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
  • x = 4/20:
    Implementation of ideas, but credit given for effort rather than merit.
  • y = 2/20:
    Irrelevant discussion/effectively blank.
  • z = 0/20:
    Blank.
Grading distribution:
Sections 70854, 70855
Exam code: finalPr0p
p: 10 students
r: 5 students
t: 7 students
v: 14 students
x: 12 students
y: 3 students
z: 0 students

A sample "p" response (from student 1223):

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