In the figure, a uniform beam with a weight of 72.1 N and a length of 3.80 m is

Question

In the figure, a uniform beam with a weight of 72.1 N and a length of 3.80 m is hinged at its lower end, and a horizontal force F of magnitude 69.0 N acts at its upper end. The beam is held vertical by a cable that makes angle theta = 23.4 degree with the ground and is attached to the beam at height h = 1. 70 m. What are the tension in the cable, the x-component of the force on the beam from the hinge, and the y-component of the force on the beam from the hinge. Number Units Number Units Number Units

Explanation / Answer

a)

Here , for finding the tension in the string ,

Balancing the moment about pivot ,

69 * 3.80 - T*cos(23.4)*1.70 = 0

T = 168.1 N

the tension in the string is 168.1 N

b)

balancing x -force on the rod ,

Fx + 69 - 168.1 * cos(23.4) = 0

Fx = 85.2 N

x-component of hinge force is 85.2 N

c)

balancing y - forces ,

Fy - 72.1 - 168.1 * sin(23.4) = 0

Fy = 138.9 N

y -component of hinge force is 138.9 N

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