Question

A bag of cement of weight 375 N hangs from three wires as suggested in Figure P5.24.

Two of the wires make angles q1 = 55.0° and q2 = 31.0° with the horizontal. If the system is in equilibrium, find the tensions T1, T2, and T3 in the wires.

can someone show me how to solve this problem?

Answer 1

It says the answer is:
T1 = 322 N, T2 = 216 N, T3 = 375 N
but why

Answer 2

the mass is in equilibrium, so the net force on the mass is zero.
so your T3 will be equal to mg, given in question = 375N

Answer 3

the knot or the point where the 3 wires meet is also in equilibrium, so the summation of force in the horizontal direction will be equal to zero, and also applies for the same for the force in the vertical direction,
\[\sum_{}^{}F _{X}=0\]\[\sum_{}^{}F _{Y}=0\]

Answer 4

so after deriving the horizontal and vertical components you will be able to find the tension on the other 2 wires

Answer 5

how do I do that?

Answer 6

1 of the horizontal components