Final answer:
The force required to create a pressure of 3.00 × 10⁹ N/m² on a nail with a 1.00 mm diameter is calculated using the area of the nail's tip and the formula F = P * A. A large pressure is achieved by exerting force over the small cross-sectional area of the nail.
Step-by-step explanation:
Calculating Force Required to Exert High Pressure on a Nail's Tip
When a hammer exerts a force on a nail, it causes the nail to penetrate into a material by exerting a large amount of pressure on a very small surface area. Pressure is defined as force per unit area, expressed as P = F/A where P is pressure, F is force, and A is area. To calculate the force necessary to create a pressure of 3.00 × 10⁹ N/m² on a nail with a circular tip of 1.00 mm diameter, we start by calculating the cross-sectional area of the nail's tip in meters squared (m²). The radius (r) is half of the diameter, so for a 1.00 mm diameter, r = 0.50 mm or 0.50 × 10 m. The area (A) of the circular tip is π*r², which equates to π*(0.50 × 10 m)².
After calculating the area, we use the formula P = F/A to find the force (F). Rearranging it to F = P*A, we plug in the calculated area and the given pressure to get the resulting force. The example provided shows that a very small area can create very high pressures with moderate forces because the area of impact is extremely small, which is typical when a hammer strikes a nail. Hammering a nail demonstrates important principles of pressure and force distribution, critical in understanding how forces applied over different areas result in varying pressures and why nails are effective in joining materials together.