Ποπάυ και Όλιβ
Brutus has kidnapped Olive and locked her in a cell high up. Surrounding it is a moat filled with crocodiles, and the only way to reach it is via a beam of length ℓ = 6 m, which is hinged around an axis located a distance d = 1 m from the end, as shown in the figure. To set a trap for Popeye, who is rushing to save Olive, Brutus has broken the mechanism that keeps the beam horizontal and instead has hung a body S1 of mass m1 = 40 kg at the end, so that as soon as Popeye steps onto the beam, it begins to rotate. Popeye realizes the trap and, before stepping onto the beam, ties object S1 to a box on the ground with mass m2 = 550 kg, with string 2 initially exerting no force on S1 but being completely vertical.
a. Calculate the weight of the beam.
b. If, at the moment Popeye reaches the end of the beam, the box experiences a force from the floor of N = 1500 N, find Popeye’s mass M1 and the force exerted by the rod on the joint.
c. After Popeye has freed Olive, they set off on their way back. However, Olive is afraid of heights, so they cannot walk separately on the beam; therefore, Popeye picks her up, but as soon as they try to step onto the beam, they see that the box lifts up, so they abandon this idea. So they hold hands, and the beam barely stays upright. Based on this, calculate Olive’s mass. (When the two are holding hands, they are 1 m apart)
Vasilis Doukatzis
