Final answer:
The magnitude of the tension in the wire supporting the uniform beam is 2160 N. Therefore, the magnitude of the tension in the wire is 2160 N.
Step-by-step explanation:
To calculate the magnitude of the tension in the wire, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the net force is the tension in the wire, the mass is 120 kg, and the acceleration is due to gravity.
The angle between the beam and the horizontal is not relevant for this calculation.
First, we need to calculate the weight of the beam, which is its mass multiplied by the acceleration due to gravity (9.8 m/s^2). The weight of the beam is 120 kg * 9.8 m/s^2
= 1176 N.
Next, we can calculate the tension in the wire.
Since the beam is in equilibrium, the sum of the vertical forces acting on it must be zero.
The tension in the wire can be found by subtracting the weight of the beam from the vertical component of the tension:
Tension = Vertical component of tension - Weight of the beam
The vertical component of tension can be calculated using the sine of the angle between the beam and the horizontal:
Vertical component of tension = Tension * sin(delta)
Substituting the values into the equation, we get:
Tension = Tension * sin(27) - 1176 N
Simplifying the equation, we have:
Tension * (1 - sin(27)) = 1176 N
Dividing both sides of the equation by (1 - sin(27)), we get:
Tension = 1176 N / (1 - sin(27))
Using a calculator, we can find that sin(27) = 0.454.
Substituting the value into the equation, we find:
Tension = 1176 N / (1 - 0.454) = 2160 N
Therefore, the magnitude of the tension in the wire is 2160 N.