by alkaline » Sat Nov 15, 2003 9:56 pm
with fred using just one hand, a box wouldn't be completely stable. But, he could balance one edge on his hand, and the other on his arm. If you consider this cheating, that means he would have to use two hands/arms.
For Bob, he can technically carry a box with one hand like Fred can, but it's less stable. When Bob adds a hand (for a total of two), one dimension is stablized (left/right), but the second dimension(forward/backward) still isn't quite as stable. However, but it isn't completely unstable - the contact area of hands with the box isn't a point, it's linear. This stabilizes the motion somewhat. To make it the most stable, bob can rest the side of the box facing him against his body.
For Emily, she can also carry a box with one hand if she's really talented at balancing. Two hands would be more stable, and i argue that it wouldn't be hard for her to do it. The left/right motion is already taken care of by holding the left & right edges of the box. The area of contact of her hands with the box takes a two dimensional shape, so her hands would stablize the other two dimensions. One of these two, the forward/back dimension, could be further stablized against the body. The second of these two would be less stable (lambda/rho) because she wouldn't be able to use her body to balance it, but if the box wasn't too heavy unbalanced she could carry it without much trouble (just as we can hold boxes away from our body). If she added two more hands to hold the lambda & rho sides, then the only semi-unstable dimension that is left could be held against the body.