Answer :
To determine the maximum force that can be safely applied to a rectangular floor tile given its dimensions and the maximum pressure it can sustain, let's follow these detailed steps:
### Step 1: Understand the given data
- The dimensions of the rectangular tile are given as:
- Length: [tex]\(1.6\)[/tex] meters
- Width: [tex]\(2.3\)[/tex] meters
- The maximum pressure the tile can sustain is given as:
- [tex]\(200 \, \text{Newtons per square meter} \, (N/m^2)\)[/tex]
### Step 2: Calculate the area of the tile
The area of a rectangle is given by the product of its length and width. Therefore, the area [tex]\(A\)[/tex] of the tile is:
[tex]\[ A = \text{length} \times \text{width} = 1.6 \, \text{m} \times 2.3 \, \text{m} \][/tex]
### Solution:
[tex]\[ A = 3.68 \, \text{square meters (} m^2 \text{)} \][/tex]
### Step 3: Calculate the maximum force
We know the relationship between pressure, force, and area is given by the formula:
[tex]\[ P = \frac{F}{A} \][/tex]
Where:
- [tex]\(P\)[/tex] is the pressure
- [tex]\(F\)[/tex] is the force
- [tex]\(A\)[/tex] is the area
Rearranging this formula to solve for force [tex]\(F\)[/tex], we get:
[tex]\[ F = P \times A \][/tex]
### Step 4: Substitute the known values into the formula
The maximum pressure [tex]\(P\)[/tex] is [tex]\(200 \, N/m^2\)[/tex], and the area [tex]\(A\)[/tex] is [tex]\(3.68 \, m^2\)[/tex]:
[tex]\[ F = 200 \, N/m^2 \times 3.68 \, m^2 \][/tex]
### Solution:
[tex]\[ F = 736 \, \text{Newtons (N)} \][/tex]
### Final Answer:
The maximum force that can be safely applied to the tile is:
[tex]\[ \boxed{736 \text{ Newtons (N)}} \][/tex]
### Step 1: Understand the given data
- The dimensions of the rectangular tile are given as:
- Length: [tex]\(1.6\)[/tex] meters
- Width: [tex]\(2.3\)[/tex] meters
- The maximum pressure the tile can sustain is given as:
- [tex]\(200 \, \text{Newtons per square meter} \, (N/m^2)\)[/tex]
### Step 2: Calculate the area of the tile
The area of a rectangle is given by the product of its length and width. Therefore, the area [tex]\(A\)[/tex] of the tile is:
[tex]\[ A = \text{length} \times \text{width} = 1.6 \, \text{m} \times 2.3 \, \text{m} \][/tex]
### Solution:
[tex]\[ A = 3.68 \, \text{square meters (} m^2 \text{)} \][/tex]
### Step 3: Calculate the maximum force
We know the relationship between pressure, force, and area is given by the formula:
[tex]\[ P = \frac{F}{A} \][/tex]
Where:
- [tex]\(P\)[/tex] is the pressure
- [tex]\(F\)[/tex] is the force
- [tex]\(A\)[/tex] is the area
Rearranging this formula to solve for force [tex]\(F\)[/tex], we get:
[tex]\[ F = P \times A \][/tex]
### Step 4: Substitute the known values into the formula
The maximum pressure [tex]\(P\)[/tex] is [tex]\(200 \, N/m^2\)[/tex], and the area [tex]\(A\)[/tex] is [tex]\(3.68 \, m^2\)[/tex]:
[tex]\[ F = 200 \, N/m^2 \times 3.68 \, m^2 \][/tex]
### Solution:
[tex]\[ F = 736 \, \text{Newtons (N)} \][/tex]
### Final Answer:
The maximum force that can be safely applied to the tile is:
[tex]\[ \boxed{736 \text{ Newtons (N)}} \][/tex]
