Question

A wooden beam with mass of 30 kg is placed over two supports. The beam is just resting on top of the supports - it is not connected to the supports. The beam is 5 meters long and 2 meters is cantilevered out over the right-hand support. How far from the right end of the beam could a 50 kg person stand before the beam tips? (Hint: Think about what happens to the left reaction force when the beam just begins to tip)

(3m separating the two supports, and 2m off the right support)

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Answer 1

let m = 30 kg
M = 50 kg

let x is distance of oerson from right end.

when the beam about to tip, the left reaction force beceomes zero.

As the beam is in equilibrium net force and net torque actin on the beam must be zero.

Apply, net torque about right support = 0

m*g*0.25 - M*g*(2 - x) = 0

m*g*0.25 - 2*M*g + M*g*x = 0

M*g*x = 2*M*g - 0.25*m*g

x = (2*M*g - 0.25*m*g)/(M*g)

x = 2 - 0.25*m/M

= 2 - 0.25*30/50

= 1.85 m <<<<<<<<<-------------------Answer