Motion System Design

# Fun with Fundamentals: Problem 242

Problem 242: Hairy Houdinis

In his heyday, Melvin the Magnificent traveled the vaudeville circuit performing his renowned magic act. From a sequined top hat to illustrious hand gestures, he conducted his show with glorious fanfare. Despite Melvin’s powerful stage presence, his assistants, three handsomely dressed monkeys, always stole the show.

But during a performance at the Hare’s Bluff Opera House, Melvin faced disaster. The show started off well. Abracadabra, who preferred to be called Abbey, carried out the rings and magic wand for his warm-up tricks and showed off her satin ball gown. Another worthy assistant, Hocus, later climbed in a box which Melvin proceeded to saw in half, not even scratching the tuxedo-clad monkey inside. Pocus was normally the best behaved of the three animals and, thus, was chosen for the disappearing monkey illusion.

Pocus disappeared all right. Just before his cue, he spotted a stage rope hanging from the ceiling and couldn’t resist climbing it. The others quickly followed suit, leaving a speechless, red-faced Melvin on stage below.

When Melvin looked up, Pocus, who weighed 20 lb, descended the rope at an acceleration of 5 ft/sec2. Below him, Abbey, who weighed 25 lb, climbed up at a constant speed of 2 ft/sec2. Under her, Hocus, weighing 15 lb, pulled himself up at an acceleration of 3 ft/sec2. With the monkeys on the move, what was the tension in the rope?

Hint: Treat the rope and monkeys as a complete system.