A beam that weighs 200 N is connected to a wall by a hinge so that...

A beam that weighs 200 N is connected to a wall by a hinge so that it makes an angle of θ = 30.0◦ with the horizontal. The beam is 1.50 m long and is held in place by a cable that runs horizontally from the end of the beam to the wall. A box that weighs 100 N hangs from the end of the beam. Calculate a) the tension in the cable connected to the wall and b) the magnitude and direction of the force exerted by the hinge on the beam.

Solutions

Expert Solution

a) We can assume that the weight of the beam passes through the middle point of the beam (0.75m away from the hinge). The force diagram is then:

Because the beam is in equilibrium, the sum of the torques about the hinge gives:

b) The force balance in the vertical and horizontal direction gives:

Then the magnitude and the direction (angle made with horizontal) of the force excerted by the hinge on the beam is:

genius_generous answered 1 year ago

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