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The World-War II battleship U.S.S Massachusetts used 16-inch guns whose barrel lengths were 15 m long. The shells each of mass 1250 kg when fired, had a muzzle velocity of 750 m/s. Assuming a constant force, determine the explosive force experienced by the shell inside the barrel. Start from a fundamental principle.

User Kreya
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1 Answer

3 votes

Answer:

The explosive force experienced by the shell inside the barrel is 23437500 newtons.

Step-by-step explanation:

Let suppose that shells are not experiencing any effect from non-conservative forces (i.e. friction, air viscosity) and changes in gravitational potential energy are negligible. The explosive force experienced by the shell inside the barrel can be estimated by Work-Energy Theorem, represented by the following formula:


F\cdot \Delta s = (1)/(2)\cdot m \cdot (v_(f)^(2)-v_(o)^(2)) (1)

Where:


F - Explosive force, measured in newtons.


\Delta s - Barrel length, measured in meters.


m - Mass of the shell, measured in kilograms.


v_(o),
v_(f) - Initial and final speeds of the shell, measured in meters per second.

If we know that
m = 1250\,kg,
v_(o) = 0\,(m)/(s),
v_(f) = 750\,(m)/(s) and
\Delta s = 15\,m, then the explosive force experienced by the shell inside the barrel is:


F = (m\cdot (v_(f)^(2)-v_(o)^(2)))/(2\cdot \Delta s)


F = ((1250\,kg)\cdot \left[\left(750\,(m)/(s) \right)^(2)-\left(0\,(m)/(s) \right)^(2)\right])/(2\cdot (15\,m))


F = 23437500\,N

The explosive force experienced by the shell inside the barrel is 23437500 newtons.

User Tamouse
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