In the diagram below, a street light m is hung from a horizonal beam; the beam i
ID: 1464810 • Letter: I
Question
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 0 = 35 degree, x2 = 3.55 m, x1 = 2.18 m, and that the mass of the street light is m = 65.1 kg, find the tension in the cable. Use 9.8 m/s^2 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.)Explanation / Answer
Let the tension in the string be T.
Taking the Pivot point ot be point P.
We can write -
Weight of beam * x2/ 2 + m*g * x1 - T*sin() = 0
108 * 9.8 * (3.55/2) + 65.1 * 9.8 * 2.18 = T * sin(35)
T = 5700 N
Tension in the cable, T = 5700 N