A nail having a tip of radius 0.02 cm is hit to create a pressure of 6Xe9 N m-2 by a hammer. What will be the energy applied on the nail. Also give explanation, How it is possible to create the force required.
Answers
Given : A nail having a tip of radius 0.02 cm is hit to create a pressure of 6 × 10^9 Nm¯² by a hammer.
To find : The energy applied on the nail and also give explanation, how it is possible to create the force required.
solution : We know, the formula of energy = pressure × volume
= 6 × 10^9 N/m² × 4/3 πr³
[ here r = 0.02cm = 0.0002 m = 2 × 10¯⁴m ]
= 6 × 10^9 N/m² × 4/3 × 3.14 × (2 × 10¯⁴m)³
= 8 × 10^9 × 3.14 × 8 × 10¯¹² Nm
= 200.96 × 10¯³ J
= 0.20096 J
as a nail is hit by a hammer. so, the force will be created with the movement of hammer which is considered as Kinetic Energy.
we know, pressure = force/cross sectional area
⇒6 × 10^9 = F/(4πr²)
⇒F = 6 × 10^9 × 4 × 3.14 × (2 × 10¯⁴)²
= 96 × 3.14 × 10
= 3014.4 N
Therefore required force is 3014.4 N