In a hydraulic press used for compressing cotton the area of the piston is `0.1 m^(2)` and the force exerted along the piston rod is `200 N`. If the area of the larger cylinder is `0.8 m^(2)`, find the pressure produced in the cylinder and the total crushing force exerted on the bale of cotton.

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the Pressure in the Smaller Cylinder
The pressure \( P \) produced in the smaller cylinder can be calculated using the formula:
\[ P = \frac{F}{A} \]
where:
- \( F \) is the force applied (200 N),
- \( A \) is the area of the piston (0.1 m²).

Substituting the values:
\[ P = \frac{200 \, \text{N}}{0.1 \, \text{m}^2} = 2000 \, \text{N/m}^2 \, \text{(or Pa)} \]

### Step 2: Use the Pressure to Find the Total Crushing Force in the Larger Cylinder
Since the pressure is transmitted equally in a hydraulic system, the pressure in the larger cylinder will also be 2000 N/m². We can find the total force \( F \) exerted on the bale of cotton using the same pressure formula:
\[ F = P \times A \]
where:
- \( P \) is the pressure (2000 N/m²),
- \( A \) is the area of the larger cylinder (0.8 m²).

Substituting the values:
\[ F = 2000 \, \text{N/m}^2 \times 0.8 \, \text{m}^2 = 1600 \, \text{N} \]

### Summary of Results
- The pressure produced in the cylinder is **2000 N/m²**.
- The total crushing force exerted on the bale of cotton is **1600 N**.

---