Question

The tip of a nail exerts tremendous pressure when hit by a hammer because it exerts a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00-mm diameter to create a pressure of 3.00×10^9 N/m²? (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)

a) 29.8 N
b) 59.6 N
c) 89.4 N
d) 119.2 N

Answer 1

To create a pressure of 3.00×109 N/m² on a nail with a 1.00-mm diameter tip, a force of approximately 59.6 N needs to be exerted, applying the area and pressure formula.

Step-by-step explanation:

The pressure a nail tip exerts when struck by a hammer can be calculated by knowing the force applied and the area over which it is distributed. Given the pressure (P) is 3.00×109 N/m² and the diameter (d) of the nail tip is 1.00 mm, the area (A) can be calculated using the formula for the area of a circle, A=πr2, where r is the radius of the circle.

First, we convert the diameter to meters (1.00 mm = 0.001 m) and then calculate the radius (r = d/2 = 0.001 m / 2). The area is then A = π (0.0005 m)2. To find the force (F), we rearrange the pressure formula P = F/A to F = P × A. By plugging in the values, we find that the force required is approximately 59.6 N.