Answer:
10,800 Nm
Explanation:
Torque is equal to the distance times the perpendicular force. For an object to have no angular acceleration, the net torque acting on the object must be zero, meaning any clockwise torques must be balanced with equal and opposite counterclockwise torques.
Draw a free body diagram of the beam. There is the weight of the beam (Mg) pulling down at its center, the weight of the worker (mg) pulling down at the far end of the beam, a reaction force (R) where the beam is bolted, and a reaction torque (τ) where the beam is bolted.
Take counterclockwise to be positive. Summing the torques on the beam about the bolt:
∑τ = Iα
τ − Mg L/2 − mg L = 0
τ = Mg L/2 + mg L
τ = gL (M/2 + m)
Plugging in values:
τ = (9.8 m/s²) (3.80 m) (430/2 kg + 75.0 kg)
τ = 10,800 Nm
