00:01
So in this question, we've got a ceiling and from which we've got a mass hanging, mass m equals 3 .3 kilograms.
00:12
And we've got two ropes pulling up with tension t1 and a tension t2 and at angles theta 1 and theta 2.
00:25
And we're told that theta 1 is equal to 40 degrees and theta 2.
00:32
Is equal to 30 degrees.
00:35
So now we've got a force downwards of mg, and we can balance horizontal forces to find out, horizontal and vertical forces to find out what these tensions are.
00:52
So by looking at horizontal forces, we get the t1 times the cosine of theta 1 is equal to t2, times the cosine of theta 2.
01:10
And by looking at vertical forces, we get the t1 times the sine of theta 1 plus t2 times the sign of theta 2 is equal to m g and we can use this to solve for the tensions.
01:28
So equations 1 and 2.
01:31
Equation 1 tells us that t1 is t2 cos theta 2 over cos theta 1 and we can put that back into equation to get that we've got t2 cos theta 2 tan theta 1 plus sine theta 2 is equal to mg so that t2 is mg over cos theta 2 tan theta 1 plus sine theta 2 so yeah so that that's right this is t2 and then i can put that back into this equation for t1, to get that t1 is going to be equal to cos theta 2 over cos theta 1.
02:22
So that means that i can divide by cos theta 2 and multiply by cos theta 1 in the denominator.
02:30
Together this is mg over sine theta 1 plus cos theta 1 tan theta 2, which makes sense because all we've really done to go from one to the other is swap 1 and 2.
02:46
So now we can calculate the tension in the left rope.
02:50
So t1 is going to be, so i'm going to just put numbers in.
02:56
So it's 3 .3 kilograms times 9 .81 meters per second squared...