A force diagram of the situation is shown below:
In order to the system is in equilibrium. It is necessary that the torque produced by the man equals the torque produced by the bucket:
τ1 = τ2
F1*d1 = F2*d2
where,
F1: force of the man = ?
d1: distance to the pivot from force F1 = 5 m
F2: weight of the bucket = 500kg*9.8m/s^2 = 4900N
d2: distance to the pivot from weight of the bucket = 0.5m
Solve the equation above for F2, replace the values of the other parameters and simplify:
F2 = (F1*d1)/d2 = (4900N)(5m)/(0.5m)
F2 = 49000N
