Chapter 4.3, Problem 2aT

Attach day to the bottom left side of the board so that it remains at rest when placed horizontally on the pivot. (The pivot should still be through the hole used in part B above.)

1. On the figure at right, mark the approximate location of the center of mass of the system composed of clay and board with an “x.”

Is the center of mass of the system located to the left of, to the right of, or along the vertical line through the pivot? Explain.

2. Suppose that the piece of clay were moved to a new location (point A) closer to the pivot.

Predict whether the board would remain in equilibrium. Explain.

Would the total mass to the left of the pivot change when the clay is moved to point A?

Check your predictions.

3. Suppose the piece of clay were moved back to its original location and additional clay were added to it.

Would the board remain in equilibrium?

Is there any location along the bottom edge of the board at which this larger piece of clay could be placed so the board will be in equilibrium? If so, is the new location closer to or farther from the pivot?

Check your prediction.

4. Generalize your observations from parts 1, 2, and 3:• Is it possible to keep the total mass to either side of the pivot unchanged yet change the system so that it is no longer in equilibrium?
• Is it possible to change the total mass to one side of the pivot and still have the system in equilibrium?
• Is it enough to know the total mass to either side of the pivot in order to determine whether the system will be in equilibrium? Explain.