Last week’s car stuck in the mud has activated the ingenuity of our astute readers, who have offered a wide range of solutions.
“I think a good option would be to surround the tree with the rope, and tie each of the ends of the rope, twisting them into the axles of each of the wheels that rotate. If the latter is expensive, tie the rope at one end to the tree and screw the other to the axle of a wheel that rotates,” suggests Salva Fuster. And it can be a good solution, if the wheels turn, the motor does not stall… and the rope does not slide over the axle without wrapping.
For his part, Ignacio Alonso believes that “the solution is to tie the car to the tree with the taut rope and push it perpendicularly in its middle.” This option has the advantage that there is no need for the motor to run or for the wheels to rotate (or for the rope to be wound, in both senses of the term); but it only allows the car to move a short distance, since the traction decreases rapidly as the angle formed by the two sections of the rope increases; although, yes, with a large initial increase in the applied force (so large that, in the case of an ideal inextensible rope, an infinite tension would be needed to ensure that a force applied perpendicularly in its half did not displace it at all).
The solution proposed by our veteran commentator Francisco Montesinos is simpler: “It seems to me that one option would be to tie one of the ends of the rope to a nearby tree with a stress-proof knot. Pass the other rope through the tow hook that almost all cars, if not all, usually carry, and then place it near the tree where we tied the knot. We would have a pulley assembled and the force applied by us to the loose end multiplied by two would equal the resistance R of the car. I believe that the tension of the rope comes, on the one hand, from the force F exerted by the person pulling the loose end, which is transmitted along the rope to the tree, but there the reaction of the tree comes into play equal to F but in the opposite direction, hence R = 2F”. Another way of saying it is that for every meter of rope you stretch, the car advances (if it advances) half a meter, so the traction force doubles. If twice your strength is enough to unblock the car, this is the best solution, and if there are several travelers all pulling the rope on the improvised pulley, it will surely work.
By the way, in his comments Montesinos mentions, as a source of ingenious solutions, the wonderful magazine Popular MechanicsSpanish version of the American Popular Mechanicswhich some of us enjoyed in our youth thanks to the Mexican and Italian editions (Meccanica Popolare). As a small tribute to the inspiring magazine (which, unfortunately, has not been published in Spanish for a long time), here is a riddle based on its DIY and household tinkering section:
When a cork stopper does not fit in the mouth of a bottle for which it was not intended, it is common to thin it by removing chips with a knife; but in this way a smooth or symmetrical surface is not achieved, so the fit is usually quite defective. Can you think of a cleaner and more efficient way to reduce the diameter of a cork stopper by a few millimeters?
And finally, a riddle proposed by Ignacio Alonso, which is a variant of a “classic” that first appeared – if my sources do not deceive me – in the book by Saul X. Levmore and Elizabeth Early Cook Super Strategies for Puzzles and Games (1981):
There are four people with a flashlight on the same floor of a ruined building. To get to the street they have to go down a narrow, rickety and dark staircase, necessarily with a flashlight, and at most two at a time, as the structure could collapse under a greater weight. The four people, of different ages and builds, move at very different speeds, and each one takes the same time to go down as to go up: 8, 4, 2 and 1 minutes respectively. How do they get everyone down in 15 minutes?
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