Write the node equations for the nodes 1 and 2 of the model of the oak beam sketched in Figure 2-32.
The model of the round beam is such that axial symmetry is assumed so that a
hemispherical section will suffice for nodes. In Figure 2-32 the node numbering scheme
follows the pattern of number 1 is in the center, 2, 3, and 4 are radially outward to the
outside surface. Then on a 22.5º rotation numbers 5, 6, and 7 occur. On the next 22.50
rotation numbers 8, 9, and 10 occur. Continuing in this pattern there are three nodes at
every 22.5º rotation for the first 28 nodes. On the next hemisphere axially parallel to the
first hemisphere node number 29 will be on the center position with numbers 30. 31.
And 32 outward. Again at a 22.5º rotation numbers 33, 34, and 35 occur. Continuing, the
pattern is such that nodes on the hemisphere parallel to the succeeding hemisphere will
have a number of the previous node plus 28. Thus, node 2 will be adjacent to nodes 29,
axially, and also to nodes 3, 5, and 1. This model is sketched. Node 1 has nine (9)
adjacent radial nodes; 2, 5, 8, 11, 14, 17, 20, 23, and 26. Node 1 also has an adjacent
node on the axis, number 29. This model is sketched.
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The Coulomb constant, k, has a value of 
The permittivity of free space,
has the units
A. 
B. N·m/C.
C. 
D. 
E. that are not given.
How many photons per second emerge from a laser of power with wavelength (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ? s)
A) 6.09 × 1015 photons/s B) 5.03 × 1012 photons/s C) 3.07 × 1015 photons/s D) 3.07 × 1013 photons/s
Which of the following is true about the seasons on Uranus?
A) The seasons on Uranus are not unlike those on Earth or Mars. B) The Uranian rotation axis produces some extreme seasonal effects. C) Like Jupiter, Uranus has little tilt, with its equator always facing the Sun. D) From the Uranian equator, the Sun would remain stationary all the time. E) Uranus' weather will become less turbulent as equinox approaches in 2049.
A polar bear starts at the North Pole. It travels 1.0 km south, then 1.0 km east, and then 1.0 km north to return to its starting point. This trip takes 45 min. What was the bear's average velocity?
A) 0.00 km/h B) 0.067 km/h C) 4.0 km/h D) 5.3 km/h