Part A In the diagram below, a street light m is hung from a horizonal beam; the

Question

Part A In the diagram below, a street light m is hung from a horizonal beam; the beam is supported by a pin at P and by the cable (cord) from the end of the beam to the upper part of the pole. Given that the beam is uniform and has a mass of 108 kg, the angle . 35, x,-3.55 m, 218 m, and that the mass of the street light is m -76.1 kg, find the tension in the cable. Use 9.8 m/s and express your answer to three significant digits. Use scientific notation. (Suggestion: Draw a free body diagram of the beam and take torques about P) cord

Explanation / Answer

here,

theta = 35 degree

x1 = 2.18 m

x2 = 3.55 m

mass of street light , m1 = 76.1 kg

mass of beam , m2 = 108 kg

let the tension in the cable be T

equating the torque about the hinge

m1 * g * x1 + m2 * g * x2 /2 - T * sin(theta) * x2 = 0

76.1 * 9.81 * 2.18 + 108 * 9.81 * 3.55/2 = T * sin(35) * 3.55

solving for T

T = 1722.84 N

the tension in the cable is 1722.84 N

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