I have a board 18" x 18" x 1/8"
I need to support it in an upright position at a 15 degree angle. How big must the base of support be to keep it from falling over.
To determine the size of the base of support needed to keep the board from falling over, we need to consider the center of mass and stability of the board. The center of mass of an object is the point at which all of its mass can be considered to be concentrated.
In this case, the board is in an upright position at a 15-degree angle. The center of mass will be located along the vertical axis at a certain height from the base. To ensure stability, the base of support should be wide enough so that the vertical line passing through the center of mass falls within the base.
To calculate the required size of the base of support, consider the following steps:
1. Identify the center of mass (COM) of the board:
- Since the board is a uniform rectangular shape, the center of mass will be in the middle of the board, vertically and horizontally.
- The board measures 18" x 18" x 1/8", so the center of mass horizontally will be at 9" from either edge, and vertically at 9" from the bottom.
2. Determine the height of the center of mass from the base:
- Since we need to support the board at a 15-degree angle, we can imagine it as a right-angled triangle formed by the board and the base of support.
- The height from the base will be the opposite side of the triangle, and the length of the board will be the adjacent side.
- Therefore, the height from the base can be calculated using the formula: opposite = adjacent * tan(angle).
- In this case, the angle is 15 degrees, and the length of the board is 18". So, the height from the base will be 18" * tan(15 degrees).
3. Calculate the required base width:
- To ensure stability, the center of mass should be within the base.
- Assuming we want the center of mass to be somewhere around the middle of the base horizontally, we can determine the necessary base width by doubling the height from the base (to cover both sides) and adding it to the width of the board.
- The required base width will be 2 * height from the base + width of the board.
By following these steps, you can find out the required base width for supporting the board at a 15-degree angle.