Dynamics supplement question 19

[JohnATL]

On problem 19(c) of the supplemental questions for AP1 Dynamics I must be doing something wrong with the Trig functions to solve for the tension in each wire, but the problem is not worked out in the answer, it simply says to substitute the appropriate trig functions to solve.  Can someone show me the steps for that so I achieve the correct answer?

Thanks!

 

 

AP1 Dynamics 19.pdf

[FizziksGuy]

Solution attached...

19c-soln.pdf

[JohnATL]

Thank you!  While waiting for your answer I discovered another shortcut that is a bit quicker, but only works when the two angles equal 90°.  Simply take the sin of each angle and multiply them times mg to get T1 and T2.  I think your solution is universal however, even if the angles don't add up to 90°.  How often do AP1 questions include this type of question where the angles don't sum up to 90°?

[FizziksGuy]

This is a very common type of question, and the process of breaking up forces on a FBD into components and applying Newton's 2nd Law carries throughout the entire course.  One of those things you've gotta learn.     The "shortcut" that you learned isn't really a shortcut, and isn't something I'd recommend, as it won't carry through to other situations in which the third force isn't caused by gravity on a mass.  I'd focus on learning how to draw free body diagrams, break forces at angles into components, and applying Newton's 2nd Law.  It's the backbone of mechanics, and very important in further units as well.  Good luck!

[JohnATL]

Thanks for the insights!  I appreciate the help.