Refers to the Newton's Third Law to answer this. States all forces between two objects exist in equal magnitude and opposite direction. Compares the force of the falling tree, FT, with the force of screwing in the bulb, FB.
Calculates FT by multiplying mass times acceleration. Googled the most likely kind of tree: oak. Claims the average mass of that to be 14,385 kilograms. Substitutes in gravity (9.8 meters per seconds squared) for acceleration. Assumes no air resistance.
FT = 14385 kg * 9.8 m/s2
FT = 140973 Newtons
Now, what is FB? Must determine the friction of the bulb's socket. Stated a stopped clock to be correct twice a day (and only twice). Indicates a dual-axis rotational force, rather than standard torque. Subtracts the circumference of the second axis, r2, from the circumference of the first axis, r1. Divides that the length of the screw, l. Gives the following equation:
FB = 2 * pi * (r1 - r2) / l
Measured r1 as 0.024 meters, r2 as 0.011 meters, and the screw as 0.05 meters. Plugs those in.
FB = 2 * pi * (.024 - .011) / .05
FB = 1.634 Newtons
Leaves one final step: how many trees does it take? Must set the forces equal. Seeks the coefficient, NT, or Number of Trees.
FT * NT = FB
NT = FB / FT
NT = 1.634 / 140973
NT = .00001159 trees
Probably amounts to a few branches. Considers how many branches a trivial exercise left to the reader.
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Why did you catch that Furret?