The Hammer-Ruler Trick
• 12-inch ruler (plastic works, but wood is preferable)
• Thick rubber band
• String (optional)
• Tape (optional)
• First, pick up your ruler and balance it lying lengthwise on your index finger. Try using the six-inch mark on your ruler as your balancing point—this is roughly the location of the ruler's center of mass, and you'll notice it's at the middle of the ruler. This is because our ruler is an object of uniform density and is shaped in such a way that it doesn't have a heavier or lighter end.
• Take your ruler and lay it flat on a table or desk. How many inches on the ruler can you nudge over the edge of the table before it falls off?Think about our hypothetical seesaw from earlier. You should find that once you nudge the ruler's center of mass over the table's edge (the fulcrum), gravity applies more torque to the more massive side of the system than the other, dragging it over the edge and onto the floor.
• Now, try to identify the center of mass on your hammer. If you hold your hammer lengthwise, can you balance it by placing your index finger beneath the point of the hammer located halfway along its length?Probably not! In fact, you should find that the hammer's head is much heavier than its handle. We can infer that the hammer's center of mass is located somewhere closer to its head.
• The goal now is to use our materials to build a new mechanical system with a center of mass located as close to the 0-inch tip of the ruler as possible. (Hint: our hammer will act as a counterweight.) Take another look at how classic Victorian balance toys are structured. Knowing what you've learned about where the hammer's center of mass is, where do you think the hammer is going to go when we build our new system?
• Loop your rubber band over your hammer so that it hangs somewhere near the middle. (Depending on how smooth the hammer handle is, you may want to affix the rubber band to the handle with tape. If your rubber band is too stretchy, you can use a loop of string approximately three inches in diameter instead).
• Loop the rubber band over your ruler. This end of the loop should hang near the 2-inch mark on the ruler. The end of the hammer's handle should intersect and form an acute angle with the ruler at around the 8-inch mark.
• Place the end of the ruler that starts with zero near the edge of the table. Does it balance? Try altering the position of the hammer's head relative to the tip of the ruler. With some careful adjustments, you can tweak the system so that its center of mass is located at the very tip of the ruler.
• Once you've gotten your system to balance, try nudging the 0-inch end of the ruler closer and closer to edge of the table. By doing so, you're moving the system's center of mass progressively closer to the fulcrum and, if you're careful, you can produce a dramatic effect by getting your system to balance on a mere sliver of the table's edge.
• Extra: If you want to create an even cooler visual effect and make your system look more like a Victorian balance toy, place a very light stuffed animal on the 12-inch end of the ruler. (A stuffed monkey that hangs onto the end of the ruler with clasped Velcro hands is a crowd favorite.)