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A hammer is used to drive a nail into a wooden floor. The hammer is bought down with a force of 200N the area of the top of the nail is 0.5cm² what pressure is put upon the top of the nail by the hammer below?

To solve this problem, we need to calculate the pressure exerted on the top of the nail by the hammer. The pressure \( P \) is given by the formula:

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

Where:
- \( F \) is the force applied by the hammer, which is 200 N.
- \( A \) is the area over which the force is applied. The area is given as 0.5 cm².

However, the area needs to be converted to square meters (m²) because the standard unit of pressure is pascals (Pa), which is equivalent to \( \text{N/m}^2 \).

1 cm² = \( 1 \times 10^{-4} \) m².

So,
\[
A = 0.5 \, \text{cm}^2 = 0.5 \times 10^{-4} \, \text{m}^2 = 5 \times 10^{-5} \, \text{m}^2
\]

Now, substituting the values into the formula:

\[
P = \frac{200 \, \text{N}}{5 \times 10^{-5} \, \text{m}^2}
\]

Let's calculate this.

\[
P = \frac{200}{5 \times 10^{-5}} = 4 \times 10^6 \, \text{Pa} 
\]

So, the pressure exerted on the top of the nail is \( 4 \times 10^6 \) pascals (Pa).

Would you like any further details or explanations on this? Here are some related questions that might interest you:

1. How does the area of contact affect the pressure applied to a surface?
2. What would happen to the pressure if the force were doubled but the area remained the same?
3. How can this concept of pressure be applied in hydraulic systems?
4. What is the relationship between force, area, and pressure in different units?
5. How does atmospheric pressure compare to the pressure calculated in this scenario?

**Tip:** Always remember to convert units to the standard SI units before performing any calculations to ensure accuracy.

Learn how to calculate the pressure exerted on the top of a nail by a hammer with a force of 200N, given an area of 0.5cm². Understand the conversion of area units and apply the pressure formula. Suitable for high school students studying physics.

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