He gives us a list of pieces that he'll need, and we scout the forest around the cave. Josh starts with the fulcrum, which is about fifty centimeters tall and rests on a sturdy wooden platform for stability. Next, he constructs the lever out of several sticks that he connects with a rough dovetail joint. It isn't very pretty, but the pieces hold together nicely with a little tree resin. He adds two move dovetail joints at the bottom of the upside-down "V" shape and adds the horizontal legs. It was made quickly, but the construction is solid. The more I watch Josh work, the more impressed I am by his skill.
We place the lever upon the fulcrum, which falls to one side. Josh quickly pulls it off and shaves down one side, so it balances. He places the lever back up on the fulcrum, but it falls to the other side. Josh repeats the shaving process several times until it balances itself at the center.
"Wow." Sakura is captivated watching him work, and I'm having trouble concentrating on anything else myself. It's almost mesmerizing how mechanical and efficient he is with his hands.
"Okay, now that we know it's balanced, let's add a weight to either side."
Josh does as I instruct, and he places a plate on either side until it reaches the knot in the horizontal part of the lever. It doesn't quite balance out, so he shaves the heavier plates down slowly until it balances.
"Perfect, now flip them around." Josh looks at me quizzically. "Put the right plate on the left side of the lever and the left plate on the right."
He moves the plates, and now the apparatus is out of balance again. I can see Josh scratching his head in confusion. I see a learning opportunity, so I try to tease the answer out of the two of them.
"So, it's balanced on one side but not the other. why is that?"
"The lever is unbalanced."
"Pull the plates off and test your idea." Josh pulls the plates off, and the lever balances out.
"We've already determined that the lever is balanced, so there must be another problem."
"Let's try shaving them down so they balance on this side," Sakura suggests. Josh looks at me for confirmation.
"Let's give it a try," I say, shrugging my shoulders. Josh shaves the plates down again and balances them. "Okay, switch them back."
The lever is unbalanced again after it is switched. Both Josh and Sakura look very confused. I give them a minute to think about it before I make a suggestion.
"Why don't we try balancing the weights on the old lever first." Josh places the weights on the old lever, and it falls unbalanced. I walk over and adjust the position of the weights so that the lever is balanced. Just looking at the bar makes it clear that the two plates are not the same distance from the center.
"The bar is balanced, right?" The kids nod their heads. "Does that mean that the plates are the same weight?"
They pause for a second and think about it.
"Yes," says Sakura. Her usual confidence is replaced with a soft trepidation.
"What do you think, Josh?"
"No."
"Well, one of you has to be correct. How can we prove which one of you is correct?" They both sit in silence while staring at the apparatus. I let them think quietly for a moment before moving on. Sliding one weight away from the fulcrum, I watch the lever fall down on that side.
"Did the plates change weight?"
"No," says Josh quickly. Sakura doesn't speak as she keeps thinking.
"Then why did the lever unbalance?"
Silence.
I take out another plate and make a stack of two weights on one side of the lever. The plan is to have the lever balanced with two weights on one side and one on the other to show how weight distribution affects our apparatus. I adjust them until it balances.
"It's balanced, so does that mean that the two plates weigh the same as one plate?"
"No." Josh is getting more confident with each answer, but Sakura still looks frustrated.
"Of course not," I answer. "Two plates are not the same weight as one plate, so something else must be going on. Sakura, come over here, please."
I make sure to involve her, so she doesn't lose interest and stop paying attention. For my next trick, I place a stack of plates on one side of the lever.
"Now, try to raise the weights." She pushes down, and the weights rise with a bit of a struggle. I have her get off the lever to move the stack closer to the fulcrum.
"Now try." Sakura pushes down on the fulcrum and the stack pops up in the air."
"Eh?!" Her shocked voice fills the cave.
"So, this is how levers work. The closer an object is to the fulcrum the less force it takes to move it. On the contrary, the further an object is from the fulcrum, the more force it takes to move." I find a long sturdy piece of wood and lay it across another piece on the ground, so one side is closer to the fulcrum.
"Josh, stand here," I say, pointing to one side of my makeshift lever.
"Sakura, is Josh heavier than you?"
"Yes!" Sakura shouts. She seems to be getting more excited about our experiments which is great.
"Now, stand on this side." I have Sakura stand on the longer end of the lever, and Josh rises into the air. "So, to make the lever balance, we can't just focus on how much weight is on each side. We also need to keep in mind how that weight is distributed. Going back to the plates, how can we make sure the weight stays the same distance from the fulcrum on each side?"
Josh walks over to the first lever and uses one plate as a measuring stick to draw a line on either side. The lever now has a divot one plates-length away from the fulcrum on either side.
"Good, now make sure the lever is balanced without any weight on it. Once it's balanced, all we need to do is keep the plates the same distance from the fulcrum to see which one is heavier." After a couple of tries, Josh manages to balance the plates, so it stays balanced no matter which side of the lever they're on.
"Perfect, now let's head back to the scale." I pick up the plates and place them near the new scale that I want to be using.