part4

PART 4: FOR WANT OF A LEVER

They reached the high hanging valley and the lake where they intended to camp while the clouds were still gathering. Heavy packs were unceremoniously dumped to the ground. The usual debate over the best place to pitch the tents ensued. Finally the lumpy, but moderately level, top of a small hill was chosen. If it rained, they didn't want to be in the low area. Brother was dispatched to refill the water bottles while the others set up the tents.
Humming a tune he made up himself, Brother wandered off in search of a stream that wasn't as silty as the lake. He found a small one trickling between the lumps of tundra covered rocks and settled down beside it. To remove dangerous parasites, silt, and other unwanted stuff from the water the family used a lightweight backpacking filter. He worked a small lever on the top up and down. The fulcrum of the lever was between his hand and the shaft of the pump, but closer to the pump. He had to push down a great distance on his end of the lever, but he did not have to apply much force to make the pump work. The force transmitted to the pump shaft was much stronger, but did not make the pump shaft move very far.

Brother prepares the water filter.

The lever worked a small piston inside the canister. As Brother pushed his end of the lever down, the lever drew the piston up creating low pressure inside the canister. Water from the stream rose up the tube to equalize the pressure. As Brother pulled the lever handle up, the lever pushed the piston down creating high pressure against newly acquired water. The water resisted the pressure with its own internal pressure which pushed out in all directions. A valve blocked it from going back out the way it had come in. The only low pressure path open to it was through a set of filters and out a second tube that deposited it into the waiting water bottle. One by one, Brother filled them all with the freshly filtered water.

The pump handle is a class 1 lever.
The fulcrum (red) is between the effort
(blue) and the load (purple). The
thickness of the arrows represents the
size of the force. The length represents
the distance over which the force acts.
        (Photograph by Ruth Kircher)

Brother carried the full water bottles down the hill to where Mother and Father were setting up a tarp for a cooking and eating area. Keeping the food away from the tents would help prevent hungry animals from bothering them in the night. Then he headed back up the little hill towards the tents. When he arrived, both tents were set up and his sisters were trying to pound the tent stakes into the lumpy ground. Heavy rocks were the only thing they could find to carry out their task.

Little Sister's hammer rock is a class 3 lever. The effort is between the fulcrum and the load. The width of the arrows represents the amount of force. The length of the arrows represents the distance over which the force acts.

Little Sister had found a hefty one that was long and flat. By holding it at one end and pounding the stakes with the other end, she was able to use it as a crude hammer. The makeshift lever pivoted at her wrist joint and her hand applied a torque to the end of the rock near the pivot. Each time she made a down stroke the far end of the rock had to move farther than the end where her hand was. So it also had to move faster. Since the part of the rock that her hand gripped did not move very fast, she was able to continue to apply her torque to it all the way through the swing. This accelerated the rock even more. This gave the far end of the rock a lot more momentum than she could have gotten from a shorter rock of the same mass. It took a lot of force to get it moving. Once it was in motion, however, it took just as much force to get it to stop. This force, it turned out, was more than the resisting ground could provide, and the tent stakes were slowly sunk into the earth by her blows. It would have been even more effective if, like a real hammer, the rock's mass had been concentrated at the far end instead of spread out along the length of the shaft. That would have given the pounding end even more momentum. But as it was it seemed to work well enough for her purposes.

Big Sister was having trouble though, Brother noted as he approached the camp site. She had not been able to find such a nice long rock. She was trying to make due with a heavy round one. She appeared to be trying to use her entire forearm as a lever, with the fulcrum at her elbow instead of her wrist. If she had been able to do this, it would have served as a hammer in the same way as Little Sister's long rock. She was finding it hard to keep her wrist locked however. When her arm bent at the wrist, she lost the advantage of the long radius as she applied torque. As a result, the momentum of her rock was not very great and the ground was able to stop the rock's movement easily. The stake did not budge no matter how many times she hit it. She looked ready to try kicking the stakes instead.

Big Sister's rock makes a very poor class 3 lever.

Brother locks his wrist and uses his arm to lengthen the distance between the effort and the load.

      "Let me try," said Brother. He was strong and wiry from his Karate classes. By clenching his muscles tightly, he was able to keep his wrist straight. This meant however that he was using a lot of his energy fighting against himself. After several swings the stake reluctantly went in. Little Sister, meanwhile, had managed to pound in all the other stakes with her more effective rock tool.
      "You guys are sloooooooow," she teased them.
Brother was about to protest, when Big Sister held out a hand and frowned up at the sky. "It really feels like it's going to do you-know-what. Let's get our stuff into the tents."
      They opened their packs, pulling out rain gear and warm clothing. Sleeping bags and pads were tossed into the tents. Now emptied, the packs were bundled up with waterproof rain covers. At least they would be ready.
      Hungry, they headed down the hill to the cooking tarp with Puppy trotting along beside them.

[References used on this page: (Macaulay and Ardley, 1998), (Steiger, 1999)] See bibliography PREVIOUS PAGE MAIN PAGE NEXT PAGE