A 3.45 kg box is suspended from a system of massless wires...

A 3.45 kg box is suspended from a system of massless wires attached to a ceiling. The first wire makes an angle of ?? = 62.4° with the ceiling, whereas the second wire makes an angle of ?? = 40.0° with the ceiling. Determine the magnitudes of the tensions in the first and second wires, T? and T?, respectively. T? = 27.0596 N T? = 16.3655 N Question Credit: OpenStax University Physics v1

Transcript

00:01 Students in this problem we have to find the tension t1 and t2 so we have given this mass which is 3 .45 kg so the downward force will be mg so we can say that this tension t3 should be equal to m g because this mass is in equilibrium so t3 will be equal to 3 .45 multiply with g which is 9 .8 beta per second square so this is 9 .8 so we can write the value of 3 so it is equal to 3 .45 multiply with 9 .8 that is equal to 33 .8 newton right now at this point if we see that this point is in equilibrium so the net force on this point should be equal to 0.

01:05 So the one component of t2 tension force will be here and this will be the horizontal component of t2.

01:15 So this angle will be theta 2.

01:17 So this is t2 cause of theta 2 and here one component of t1 which is t1 cause theta 1 and here another component which is t1 and sine theta 1 in the upper direction and due to t 2 here t 2 sine theta 2 in the upward direction right so the net force on this point should be equal to 0 so we can say that t1 cos theta 1 should be equal to t 2 cost theta 2 right so we can say that t 1 into cos theta 1 is cos 62 point 4 should be equal to t 2 cost 40 so we will get cost 40 divided by cos 62 .4 that is equal to 1 .65 so we can say t1 upon t2 is equal to 1 .65 okay now if we see in the vertical direction this t3 should be equal to t1 sine theta 1 plus t 2 sine theta 2 so we can say t 3 will be equal to t1 sine theta 1 plus t 2 sine theta 2 so t 3 is equal to 33 .8 newton and this is t 1 into sine theta 1 which is sine 62 .4 right that is equal to 0 .866 plus t 2 sine theta 2 which is sine 40 right that is equal to t 2 into 0 .643 okay so from here we can say t 1 should be equal to t 2 times 1 .65 we will put this value here so we can write 33 .8 should be equal to t2 into 1 .65 into 0 .6 5.

03:47 866 plus t2 into 0 .643.

03:54 So this t2 4 should be equal to 33 .8 divided by 1 .65 into 0 .866 plus 0 .43...

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