Here is a logic (or lateral thinking) puzzle a friend recently asked me. (I'm going from memory, so anyone who knows this puzzle might know it a little differently) You have three balls each weighing 1kg (their mass, so 1N of weight). You have to cross a bridge which can only take your weight plus 1kg and will only survivie one journey (must be an old bridge). How do you get three balls across? ANSWER IS BELOW. TAKE A MINUTE TO THINK ABOUT IT FIRST. You juggle the balls. I guess the fact that they were balls was a hint. If you juggle the balls then your weight is always at most your own weight plus 1kg. So you can cross the bridge in one go. That's the logic. When my friend told it to me, I decided to be pedantic and asked if the weight will ever be more than my weight plus one newton. For instance, if I weigh 80kg, at any moment I have one ball in a hand so the total weight pressing down on the rickety bridge is 81kg. But as I throw that ball in the air, by conservation of momentum, an added force is thrust downward. Before throwing, the vertical momentum of me and the ball is zero. At the instant of throwing, the ball's momentum is 1N*v = v kgm/s( v is its velocity upwards in m/s, say), so the moment downwards is -v. Lets say the impulse of me throwing the ball is I=v/t for some small time t. Does this imply an impulse downards of -I? I think so. So then for that time t, the downward force is my weight plus I = 80+I N. If I throw the ball up at 10m/s (not inconceivable) with the force lasting uniformly for 1/10th of a second then the weight becomes 80+100 =180N. The bridge breaks. Being a pedant I explained this to my friend and we had an argument over it. Am I right?
Yes. In fact, this is a big part of umm... testing track shoes. They place a scale in (Yes, literally, in) the ground and have runners dash by, hitting the scale as they pass. Some folks have been known to exert over a Whopping 1,000 pounds on the scale! ETA: Correction, the momentum downwards will be - Gravity. The ball, at reaching it's peak starts at a rest stop from that height. Then calculate the downward force from that height at 9.8m per second squared. Sorry, I had skimmed your post. If you're walking and throwing the weights into the air, you'll need to calculate the arc. http://cnx.org/content/m13837/latest/
Well, I was considering throwing the balls, not catching them. I think even the act of throwing a ball upwards will break the bridge. Downwards, when the ball hits my hand it will do so at 9.8m/s^2, with a force of 9.8N. So I guess it still breaks the bridge. But taking it to another level of pedantry, wouldn't the muscles, sinews and fat of my arm, torso and legs absorb much of this force? Would it reach the bridge surface at all? Throwing the ball upwards creates a downward momentum on my arm, but I can turn my body to deflect that into somewhat horizontal force, can I not? Also twisitng my arm as I throw minimzes recoil.
Yes, it would add more force downward (For every action, there is an equal and opposite reaction). Stupid bridge. There's just no pleasing it, is there? Yes, but not significantly. The friction of the thrown weight in the air would affect the total outcome. But the effect is slight enough to be ignored for this exercise. Yes, you can redirect the forces but not perfectly. You would need to redirect ALL the force to either side, according to how the puzzle is worded. Any amount of force would break the bridge if it exceeds your mass plus 1kg. When you are redirecting the force by twisting, you'll also have to redirect the force downwards behind you at an angle. So that force still gets put to the bridge. Plus- You might throw your back out.
There IS a solution to the puzzle however, so don't give up hope. Please Register or Log in to view the hidden image! Highlight below to see Solution. The solution is this: Pick up one of the balls. Leave the other two on the ground before the bridge. Carefully walk across the bridge holding your ball steady. Upon reaching the far side, deposit your ball on the ground. Then turn and do this --: See? Easy. Problem solved.
