A Balancing Act

RAY: Let's look at this puzzler for a second. On the right-hand side of the fulcrum we've got six feet of board. That six feet of board weighs 27 pounds.

TOM: How did you figure that out?

RAY: Well, it was three times as long as the two feet of board, which weighs nine pounds, and 9 and 27 add up to 36.

So, we have 27 pounds of board on the right-hand side of our fulcrum, and if we try to figure out how much torque that exerts, it is 27 pounds times not six feet but three feet, which is the center of mass of that piece of board.

TOM: Yeah, it's like 27 pounds pushing down at three feet from the fulcrum.

RAY: Exactly-- which is 81 pound feet. Now look at the other side. On the other side of the board, we have a two-foot section that weighs nine pounds, but that two-foot section has a center of mass which is one foot from the fulcrum. So, that piece of board only has a torque of nine times one or nine pound feet.

TOM: How about the block?

RAY: The block is 48 pounds. And its center of gravity is a foot and a half from the fulcrum. So, it's 48 times a foot and a half which comes out to be, are you ready for this, 72 pound feet.

TOM: Seventy-two and nine makes 81.

RAY: Hard as it is to believe, it's balanced just the way it is.

Do we have a winner?

TOM: We certainly do have a winner, and the winner has a name, and his name is Jonathan DiMauro from Mansfield, Massachusetts. For having his answer selected at random from among all the correct answers that we got he's going to get a $26 gift certificate to the Shameless Commerce Division of cartalk.com.

[ Car Talk Puzzler ]