A 1220-N uniform beam is hinged at a vertical wall at one end and is supported b
ID: 1467094 • Letter: A
Question
A 1220-N uniform beam is hinged at a vertical wall at one end and is supported by a cable that is attached to the beam at the other end. A 200-kg load hangs at the end of the beam. The lower end of the beam makes an angle of 30 degree above the horizontal, while the supporting cable is attached to the wall at an angle of 40 degree, as shown. Calculate the magnitude of the tension in the supporting cable. Determine the vertical and horizontal components of the reaction force exerted on the beam at the hinge.Explanation / Answer
As the beam is in equilibrium, net force and net torque actin on the beam must be zero.
Let L is the length and T is the tesnion in the string.
Apply, net torque acting on the beam about pivot = 0
T*L*sin(90) - 1200*(L/2)*sin(30) - 200*9.8*L*sin(30) = 0
T - 1200*0.5/2 - 200*9.8*0.5 = 0
T = 1200*0.5/2 + 200*9.8*0.5
= 1280 N <<<<<<<<----------------Answer
B) Let Fx and Fy are forcee exerted by pivot on the beam.
Apply, Fnetx = 0
Fx - T*cos(60) = 0
Fx = T*cos(60)
= 1280*cos(60)
= 640 N <<<<<<<<----------------Answer
Apply, Fnety = 0
Fy + T*sin(60) - 1200 - 200*9.8 = 0
Fy = 1200 + 200*9.8 - 1280*sin(60)
= 2051.5 N <<<<<<<<----------------Answer
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