Abag of cement weighing 325 n hangs in equilibrium from three wires. two of the wires make angles of theta1=60.0 degrees and theta2=40.0 degrees with the horizontal. assuming the system is in equilibrium, find the tensions of t1, t2, and t3.

The sketch of the system is: two strings, 1 and 2, are attached to the ceiling and to a third string, 3.The third string holds the bag of cement. 

The free body diagram of the weight with the string 3, drives to the tension T3 = weihgt => T3 = 325 N

The other free body diagram is around the joint of the three strings.

In this case, you can do the horizontal forces equilibrium equation as:

T1* cos(60) - T2*cos(40) = 0

And the vertical forces equilibrium equation:

Ti sin(60) + T2 sin(40) = T3 = 325 N

Then you have two equations with two unknown variables, T1 and T2

0.5 T1 - 0.766 T2 = 0

 0.866 T1 + 0.643T2 = 325

When you solve it you get, T1 = 252.8 N and T2 = 165 N

T1 = 252.8 N, T2 = 165N, and T3 = 325N

 

Ifound this on google “two vectors are equal if they have the same magnitude and direction. they are parallel if they have the same or opposite direction. we can combine vectors by adding them, the sum of two vectors is called the resultant.” i hope this you.