Question

The historic stanley center for the arts in utica, new york is the proud owner of the world’s largest led chandelier. the chandelier is 35 feet wide, 17 feet tall and has a mass of 2870 kg. it is directly supported by four cables which make an angle of 63.1° with the horizontal. determine the tension in the cables.

Answer 1

The tension in each of the four cables supporting the chandelier is calculated using the weight of the chandelier and the angles the cables make with the horizontal. By applying physics formulas for weight and trigonometric functions to find the tension, the necessary values can be determined. The tension in the cables supporting the chandelier is 17165 N.

Step-by-step explanation:

To determine the tension in the cables, we can use the concept of equilibrium. Since the chandelier is directly supported by four cables, the tension in each cable must balance the weight of the chandelier. The weight of the chandelier can be calculated using the formula:

Weight = mass * gravity

where mass is 2870 kg and gravity is 9.8 m/s^2. Therefore, the weight of the chandelier is 2870 kg * 9.8 m/s^2 = 28126 N.

Since four cables are supporting the chandelier, each cable carries one-fourth of the weight.

The tension in each cable can be calculated using the equation:

Tension = Weight / (2 * sin(angle))

where the angle is 63.1°.

Substituting the values, we get:

Tension = 28126 N / (2 * sin(63.1°)) = 17165 N.