Question

Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00mm diameter to create a pressure of 3.00×10⁹ N/m²?

1. 4.91 N
2. 7.85 N
3. 12.57 N
4. 19.85 N

Answer 1

The force that must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of 3.00 × 10⁹ N/m² is approximately 2.36 N.

Step-by-step explanation:

To calculate the force exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of 3.00 × 10⁹ N/m², we can use the formula:

Force = Pressure x Area

First, we need to find the area of the circular tip:

Area = π x (radius)²

Given that the diameter is 1.00 mm, the radius can be calculated as 0.5 mm (or 0.0005 m). Thus, the area is:

Area = π x (0.0005 m)² = 7.85 × 10⁻⁷ m²

Now we can calculate the force:

Force = (3.00 × 10⁹ N/m²) x (7.85 × 10⁻⁷ m²) = 2.36 N

Therefore, the force that must be exerted on the nail is approximately 2.36 N.