A projectile weighing 2 kg flies out of the gun barrel horizontally at a speed of 1000 m / s.

A projectile weighing 2 kg flies out of the gun barrel horizontally at a speed of 1000 m / s. Determine the force of the pressure of the powder gases, considering it constant if the barrel length is 3.5m?

Given:

m = 2 kilograms is the mass of the projectile;

v = 1000 m / s – velocity of the projectile at the exit from the gun;

L = 3.5 meters – gun barrel length.

It is required to find the force of the pressure of the powder gases F (Newton).

Let’s find the acceleration that imparts the force F to the projectile.

L = a * t ^ 2/2 = a * v ^ 2 / (2 * a ^ 2) = v ^ 2 / (2 * a), hence:

a = v ^ 2 / (2 * L) = 1000 ^ 2 / (2 * 3.5) = 1,000,000 / 7 = 20408 m / s ^ 2.

Then the pressure force of the powder gases will be equal to:

F = m * a = 2 * 20408 = 40816 Newtons or approximately 41 kN.

Answer: the force of pressure of the powder gases is 40816 Newtons (approximately 41 kN).