A force of 500 N is applied to a small piston of a hydraulic press. What would be the force resulting on the big piston, if the diameter of the small piston is 6.2 cm and the area of the big piston is 126 cm2? 

To solve this problem, we'll use the principle of hydraulic presses, which states that the pressure applied on one piston is equal to the pressure on the other piston.

### Step 1: Calculate the area of the small piston
The formula for the area \( A \) of a circle is:

\[
A = \pi \times r^2
\]

where \( r \) is the radius of the circle.

Given the diameter of the small piston is 6.2 cm, the radius \( r \) is:

\[
r = \frac{6.2 \text{ cm}}{2} = 3.1 \text{ cm}
\]

So, the area \( A_s \) of the small piston is:

\[
A_s = \pi \times (3.1)^2 \text{ cm}^2
\]

\[
A_s \approx 3.14 \times 9.61 \text{ cm}^2 = 30.18 \text{ cm}^2
\]

### Step 2: Calculate the pressure on the small piston
Pressure \( P \) is defined as force \( F \) divided by area \( A \):

\[
P = \frac{F}{A}
\]

Given the force applied on the small piston is 500 N:

\[
P = \frac{500 \text{ N}}{30.18 \text{ cm}^2}
\approx 16.57 \text{ N/cm}^2
\]

### Step 3: Calculate the force on the big piston
The pressure on the big piston \( P \) is the same as the pressure on the small piston. Therefore, the force \( F_b \) on the big piston can be calculated using the area \( A_b \) of the big piston:

\[
F_b = P \times A_b
\]

Given the area of the big piston is 126 cm²:

\[
F_b = 16.57 \text{ N/cm}^2 \times 126 \text{ cm}^2 
\]

\[
F_b \approx 2087.82 \text{ N}
\]

### Final Answer:
The force resulting on the big piston is approximately **2087.82 N**.

Would you like further details or have any other questions?

---

1. What is the principle behind hydraulic presses?
2. How does the area of a piston affect the force in a hydraulic system?
3. What assumptions are made when applying Pascal's Law in this context?
4. How would the force on the big piston change if the diameter of the small piston was increased?
5. How does the shape of the piston influence the force output in a hydraulic press?

**Tip:** In hydraulic systems, even a small force applied on a small piston can generate a much larger force on a larger piston due to the difference in areas.

Learn how to calculate the force on a big piston in a hydraulic press problem. Understand the principles of hydraulic systems, including Pascal's Law and the relationship between pressure, force, and piston areas. Detailed step-by-step solution provided.

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