A cannnonball of 5 kg acts as a piston in a cylinder of 0.15 m diameter. As the gunpowder is bur

step 1 So in this problem, we want to find the acceleration of a cannon ball that's shot out of a canno

A cannnonball of 5 kg acts as a piston in a cylinder of 0.15...

A cannnonball of $5 \mathrm{kg}$ acts as a piston in a cylinder of $0.15 \mathrm{m}$ diameter. As the gunpowder is burned, a pressure of $7 \mathrm{MPa}$ is created in the gas behind the ball. What is the acceleration of the ball if the cylinder (cannon) is pointing horizontally?

Key Concepts

Newton's Second Law (F = ma)

Newton's Second Law is a fundamental principle stating that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In problems involving pressure and force, this law is used to relate the force derived from the gas pressure to the acceleration of the object (i.e., the cannonball), using the equation a = F/m. This principle is the cornerstone for analyzing the motion of objects under the influence of forces.

Cross-sectional Area

The cross-sectional area refers to the area of the face of the piston (or cannonball) which is exposed to the gas pressure. The area is calculated using the formula for the area of a circle, A = ?r², where r is the radius of the cylinder. Understanding this concept is crucial as it directly ties the geometric dimensions of a system to the force that can be generated from a given pressure.

Pressure

Pressure is defined as force per unit area. In the context of gas pressure acting on a piston or cannonball, it is the measure of the internal force that the gas exerts uniformly over the surface area of the piston. This concept is essential for understanding how a gas can drive a projectile using the force generated by its high pressure behind the projectile.

Force from Pressure

This concept involves calculating the force exerted by a pressure acting over a specific area. The equation F = P × A states that the force is the product of the pressure (in Pascals) and the area (in square meters) of the surface on which it acts. This is a key concept in deriving the mechanical acceleration of objects in systems where a pressure difference is applied.

Transcript

Please give Ace some feedback