00:01
For this problem on the topic of newton's laws, we want to calculate the tension in each chord in the figure as shown if the weight of the object that is suspended is w.
00:13
So before we start, we'll let our vertically upward direction be positive y and to the right as our x axis.
00:25
So plus x.
00:28
For part a, we know that the tension in chord c, tc, is equal to w.
00:36
We also know that we can balance the vertical components of the retention so t a sign of 30 degrees plus t b sign of 45 degrees must equal to the tension called c tc which is w balancing the horizontal components we have t a times the cosine of 30 degrees minus t b times the cosine of 45 degrees is equal to 0.
01:23
Now for the long two equations since sine 45 degrees is equal to cost 45 degrees, we add the two equations and we get t a into the cosine of 30 degrees plus the sign of 30 degrees is equal to w.
01:50
And so from here, we can find the tension in chord a in terms of w.
01:55
So t -a is equal to w over everything in the bracket, which is 1 .366.
02:03
And so we get t -a to be 0 .732 times w...