When a 22 -caliber rifle is fired, the expanding gas from...

When a 22 -caliber rifle is fired, the expanding gas from the burning gunpowder creates a pressure behind the bullet. This pressure causes the force that pushes the bullet through the barrel. The barrel has a length of $0.61 \mathrm{~m}$ and an opening whose radius is $2.8 \times 10^{-3} \mathrm{~m}$. A bullet (mass $=2.6 \times 10^{-3} \mathrm{~kg}$ ) has a speed of $370 \mathrm{~m} / \mathrm{s}$ after passing through this barrel. Ignore friction and determine the average pressure of the expanding gas.

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Key Concepts

Work-Energy Principle

This principle states that the work done by forces on an object results in a change in its kinetic energy. In the context of a bullet being propelled through a barrel, the work done by the expanding gas (through pressure acting over the distance of the barrel) is converted into the kinetic energy of the bullet. This concept is central to solving problems where force, displacement, and changes in motion are interrelated.

Relationship Between Pressure and Force

Pressure is defined as the force exerted per unit area. When a gas expands behind a bullet, it exerts a force over the cross-sectional area of the barrel. This relationship allows us to calculate the force acting on the bullet by multiplying the pressure by the area. In turn, this force, acting over the length of the barrel, does work on the bullet, linking the concepts of pressure, force and energy.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion and is given by the expression (1/2)mv², where m is mass and v is velocity. In the scenario of a bullet being fired, the bullet's kinetic energy at the moment it leaves the barrel is a direct result of the work done by the expanding gas. Understanding kinetic energy is crucial when applying the work-energy theorem to determine the effects of forces acting over a distance.

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