Christmas Decoration Vector

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I have yet another Vector question that needs to show working, the answer is provided below. Can anyone help?

Like with the previous question, I’ve attempted to do this question several times, but I can’t the answer! Can someone please show working for this question?

Well, first of all, you know that both ropes will have to support the weight of the tree (5 kg * 10 m/s^2 = 50 N) in the vertical direction. You also know that since there is no movement in the x direction, the x components of the tension in the ropes must add to give 0. With that information and a bit of trigonometry you end up with a system of two equations that you can solve to get the answer you’re looking for.

Call rope 1 a and rope 2 b. Then:

1. a*sin52 + b*sin40 = 50 N (y-component)

2. a*cos52 – b*cos40 = 0 (x-component)

1 –> a = (50N – b*sin40) / sin52

2 –> [(50N - b*sin40) / sin52]*cos52 – b*cos40 = 0

2 –> 1.268b = 39.0643

–> b = 30.8 N

–> a = (50 N – 30.8*sin40) / sin52

–> a = 38.33 N, or approximately 38 N

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