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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.)

Respuesta :

Answer:

Force, F = 2714.33 N

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, [tex]P=2.4\times 10^9\ N/m^2[/tex]

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

[tex]P=\dfrac{F}A}[/tex]

[tex]F=P\times \pi r^2[/tex]

[tex]F=2.4\times 10^9\ N/m^2 \times \pi (0.0006\ m)^2[/tex]

F = 2714.33 N

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

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