Final answer:
The force required to exert a pressure of 3.00×109 N/m² with a nail of 1.00 mm diameter can be calculated using the pressure formula F = P × A. This involves computing the area of the nail's circular tip and applying the given pressure value to find the force.
Step-by-step explanation:
The question asks about the force necessary to create a specific pressure using a nail with a certain diameter. Pressure is defined as the force exerted over an area. To find the force exerted by the nailer using very thin nails, you need to use the formula for pressure (P = force/area).
Given the pressure P is 3.00×109 N/m² and the diameter of the nail is 1.00 mm, you first calculate the area of the nail's tip, which is a circle. The radius (r) is half the diameter, so r = 0.5 mm = 0.0005 meters.
The area A of a circle is πr2, therefore A = π(0.0005 m)2. To find the force (F), you rearrange the pressure formula to F = P × A. By plugging in the given values, you can calculate the force required for the specified pressure.
In woodworking and carpentry, understanding such principles is crucial to effectively using tools like nailers and understanding the mechanics of how nails interact with materials, such as why gripping a nail with pliers prevents bending. Moreover, knowledge of pressure and force can help in estimating the usage of nails based on changes in the weight of a box of nails, reflected in the stretching of a spring scale.