To determine the maximum force that can safely be applied to the tile, follow these detailed steps:
1. Identify the dimensions of the tile:
- The length of the tile is given as 1.6 meters.
- The width of the tile is assumed to be the same since no other width is given, making it a square tile with a width of 1.6 meters.
2. Calculate the area of the tile:
- Area of a rectangle (or square in this case) is calculated by multiplying the length by the width.
[tex]\[
\text{Area} = \text{length} \times \text{width}
\][/tex]
Substituting the given dimensions:
[tex]\[
\text{Area} = 1.6\ \text{meters} \times 1.6\ \text{meters} = 2.56\ \text{square meters}
\][/tex]
3. Determine the maximum pressure the tile can sustain:
- The given maximum pressure is 200 Newtons per square meter.
4. Calculate the maximum force:
- Using the formula that relates pressure, force, and area:
[tex]\[
\text{Pressure} = \frac{\text{Force}}{\text{Area}}
\][/tex]
Rearrange the formula to solve for Force:
[tex]\[
\text{Force} = \text{Pressure} \times \text{Area}
\][/tex]
Substitute the maximum pressure and the area of the tile:
[tex]\[
\text{Force} = 200\ \text{N/m}^2 \times 2.56\ \text{m}^2 = 512\ \text{Newtons}
\][/tex]
Therefore, the maximum force that can safely be applied to the tile is:
[tex]\[
\boxed{512\ \text{Newtons}}
\][/tex]
