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 (in N) must be exerted on a nail with a circular tip of 1.20 mm diameter to create a pressure of 2.40 x 10^9 N/m^2? (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance. Enter the magnitude.)

Answer 1

Force, F = 2714.33 N

Step-by-step explanation:

It is given that,

Diameter of the circular tip, d = 1.2 mm = 0.0012 m

Radius, r = 0.0006 m

Pressure acting on the hammer,
`P=2.4* 10^9\ N/m^2`

Let F is the force exerted on a nail. It can be calculated using the definition of pressure exerted. Its formula is given by :

`P=\frac{F}A}`

`F=P* \pi r^2`

`F=2.4* 10^9\ N/m^2 * \pi (0.0006\ m)^2`

F = 2714.33 N

So, the force exerted on a nail 2714.33 N. Hence, this is the required solution.