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Mechanical puzzle?
Looking for the simplest, most clearly expressed answer to the following. Design the fittings that attach one end of a horizontal beam to a vertical wall, such that the system has the following characteristics:
When unloaded, the beam is horizontal.
When loaded with a weight at the tip, beam is horizontal (with some bending).
When loaded with the same weight at the root, beam detaches from the wall.
Beam and wall fittings are rigid one-piece devices, one welded to the beam, one to the wall; thus no moving parts like levers, springs, etc.
2 Answers
- KesLv 72 decades agoFavorite Answer
Interesting puzzle. Let's talk aboout a rigid beam projecting from a wall first. If there is a weight downward anywhere on the beam, it will produce a shear force and if the weight were sufficient the beam would be cut off at the wall (shear) as though a knife passed downward through it flush with the wall because this is where the downward beam force is resisted by the upward force of the wall.
If the weight is at the end of the rigid beam it tends to rotate the beam downward at the base as though there were a hinge there but the wall produces a counter-rotary force resisting motion. The "moment" equals the weight times the distance from the wall and decreases to zero at the wall.
Therefore your beam must consist of fittings that will resist shear at all times but release when the moment is reduced to zero at the wall. Assuming the fittings can be greased to reduce friction to nearly zero, the beam fitting should catch the wall at the top like placing your hand up into a drawer handle to open it. The lower fitting should be an inclined outward and downward plane such when there was insufficient moment to rotate the beam against the wall, the base of the beam will start to slide down the ramp. There could be several configurations of hardware to achieve the same effect.
- BRUZERLv 42 decades ago
A device that is slotted at the wall and a ball shape at the beam. The ball shape may be fitted into the bottom of the slot and slid up. The space between the ball and beam end, the neck, will hold in the slot from the weight of the beam. A weight at the end of the beam will hold the beam even firmer. But when the weight is placed at the base of the beam it will push the beam out the bottom of the slot. There should be a slide the ball will ride upon such that it allows for the ball to bury through to the neck, and wedge in at the top. When the weight is placed at the base the ball will slide right out. Picture the slot to be shaped like a typical cartoon keyhole but upside-down. If inside the slot, if you were small enough, you would be on the top of a slide at top and would slide out at the bottom.
