Submitted by carpetguy on Mon, 11/13/2017 - 11:34
Regarding question 2 of the STEP II Mechanics modules (found here: https://maths.org/step/sites/maths.org.step/files/s2s3/Mechanics_questio...)
(solutions here: https://maths.org/step/sites/maths.org.step/files/s2s3/Mech_solutions_0.pdf)
The solutions resolve horizontally and vertically, and caution extreme care in the following (quite busy) algebra. The method I used, which I find to be much more elegant and simple (and I thought I'd point out just to let others know), was to resolve parallel and perpendicular to the rod. This results in two equations (involving no angle additions within trig functions) from which an expression for cot(a) can be determined through divided one by the other.
If one of the remaining variables (T or R) is then substituted with an expression found using moments about A, the problem becomes a simple one or two liner in rearranging for the given answer.
Maybe a bit late but
spoilers?
Thanks!
There is usually more than one way to tackle a STEP question, and some are often easier than others. We sometimes show less elegant solutions to demonstrate that sometimes "brute force and ignorance" is enough rather than a clever idea.
Always useful to highlight other methods though!