Final answer:
To determine the force exerted on a nail tip to create a given pressure, one must use the formula F = P × A, considering the area based on the diameter of the nail's tip and the pressure applied.
Step-by-step explanation:
The question regarding the force exerted on a nail tip involves applying the concept of pressure in physics.
The formula for pressure (P) is P = F/A, where F is the force and A is the area over which the force is distributed.
To find the required force (F), we rearrange the formula to F = P × A. Given a pressure of 3.00 × 10⁹ N/m² and a circular tip with a diameter of 1.00 mm (0.001 m), we first find the radius (r = diameter/2) and calculate the area using A = πr². Substituting the values we get, A = π × (0.001/2) m) ². After calculating the area, we then multiply by the given pressure to find the force.
It's important to note that the high pressure is a result of the hammer bringing the nail to rest in a very short distance, which concentrates a large force onto a small area, resulting in high pressure. This is a common principle applied in mechanics and material physics.