Question

A
man with mass 80 kg begins walking out to the end of a 5 m long
beam that is supported by a hinge attached to a building at one end
and a cable that makes a 30° to the horizontal at the other end.
This cable can withstand 2000N of tension until it breaks.

a) How far can the man walk before the cable breaks?

b) Just when the cable snaps, what is the angular velocity?
Assume the only force acting on the beam are the hinge force and
its own weight. The moment of inertia of the beam is (1/3)ML^2
where M is mass and L is length.

Answer #1

(a) Let the man be at a distance x from the building then, at static equilibrium the clockwise moment about A due to tension in the spring and anti-clockwise moment due to the weight of the person. (the long beam is considered massless, since no info about mass is given).

The max tension possible is 2000N, Hence we can write,

(b) When the cable snaps the force acting on the beam is the weight of the beam. (We will be taking moment about hinge, so hinge forces will not have any moment). (Not considering the weight of the person as the question says we have to only consider the weight of the beam)

Also, the initial angular velocity just when the cable snaps will be zero but there will be an initial angular acceleration just when the cable snaps, which can be calculated by the equation,

(torque about the hinge).

This is the amount of initial angular acceleration.

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