A street lamp weighs 150 N. It is supported by two wires that form an angle of 120 degrees with each other..?

Question

A street lamp weighs 150 N. It is supported by two wires that form an angle of 120.0 degrees with each other. The tensions in the wires are equal.

a. What is the tension in each wire supporting the street lamp?

b.If the angle between the wires supporting the street lamp is reduced to 90 degrees, what is the tension in each wire.

Please help I need help.
I don't understand it.

Answer 1

150/2 = T * sin (45)
therefore T = 75/sin(45) = 88.1416022

Answer 2

Any system...let me repeat...any system that is not accelerating (or decelerating) has balanced forces acting on it so that the net force (f) is exactly zero. This results because f = ma = 0 if and only if a = 0 for a mass m.

OK your weight W = 150 N is not accelerating, in fact it is static; so there is no motion whatsoever. So f = 0 = ma for the system, which includes the weight and the two wires. This means that something is canceling out the weight because f = ma = W - F = 0; where F is that "something" canceling the weight (W).

The only "something" you've defined for your system is the forces pulling up by the attached wires. Since there are two wires, each one has a share of that upward force. By "upward" we mean vertical force acting in a direction opposite of the weight (W).

As there are 120 deg between the two wires, the vertical force for both wires is W cos(60) = Fv and for each individual wire, it's Fv/2 = (W/2) cos(60). Similarly, the horizontal force on each wire is Fh = (W/2) sin(60).

Since the vertical and horizontal forces form a right angle for each wire, the force along each wire, the tension, is T = sqrt(Fv^2 + Fh^2). And, by substitution, T = sqrt((W/2)^2 cos(60)^2 + (W/2)^2 sin(60)^2) = sqrt[(W/2)^2 [sin(60)^2 + cos(60)^2]] = sqrt((W/2)^2) = W/2.

a. Thus, the tension (T) in each wire is one half the weight of the street lamp = W/2.

b. Following the same line or reasoning used to find the tension at 120 deg, we see that the angle makes no difference because sin(deg)^2 + con(deg)^2 = 1.0 no matter what deg is. Tension, therefore, will still be W/2 in each wire with 90 deg between them.

The important thing to remember is that, if the system is not accelerating or decelerating, the net force on it is zero. So all the forces acting on it will cancel out.

Answer 3

once again components. Check my updated answer for the first inclined plain question also.