Question

A rocket works by expelling gas (fuel) from its nozzles at a high velocity. However, if we take the system to be the rocket and fuel, explain qualitatively why a stationary rocket is able to move.

Short answer

Answer: A stationary rocket is able to move when its engine ignites because the expulsion of gas (fuel) at high velocity causes the rocket to gain an equal and opposite momentum, following the conservation of momentum principle and Newton's third law of motion. The rocket then acquires a velocity in the opposite direction, causing it to move.

Step-by-step solution

Understand the principle of conservation of momentum

Conservation of momentum states that in a closed system (no external forces at play), the total momentum before an event is equal to the total momentum after that event. Mathematically, we can represent it as: $$ \sum p_{before} = \sum p_{after} $$ Where \(\sum p_{before}\) is the total momentum before the event and \(\sum p_{after}\) is the total momentum after the event.

Apply conservation of momentum to the rocket and fuel system

When we take the rocket and fuel as one system, we can apply the conservation of momentum principle. Initially, the rocket is stationary, meaning that its total momentum, a product of mass and velocity, is zero. When the rocket engine ignites, it expels gas (fuel) at a high velocity. This action causes the fuel to have a momentum in one direction, let's say to the left.

Equal and opposite momentum change

According to the conservation of momentum, if the expelled fuel has gained momentum in one direction (left), the remaining part of the system (the rocket) must gain an equal and opposite momentum in the other direction (right). That means the rocket will now have momentum in the rightward direction, and since momentum is a product of mass and velocity, the stationary rocket will now have a velocity in the rightward direction, causing it to move. This is often explained using Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In conclusion, a stationary rocket is able to move when the engine ignites and expels gas (fuel) because it gains an equal and opposite momentum, following the conservation of momentum principle and Newton's third law. The expulsion of fuel causes the rocket to move in the opposite direction.

Key concepts

Newton's Third Law of Motion

Newton's third law of motion is a fundamental principle that can explain a multitude of phenomena in the everyday world, including the flight of a rocket. Simply put, it states: For every action, there is an equal and opposite reaction. This means that forces always come in pairs.
When a rocket engine fires, it exerts a force on the expelled gas, pushing it backward. By Newton's third law, the gas must exert an equal but opposite force on the rocket, pushing it forward. This is what propels the rocket through space. The forces are equal in magnitude but opposite in direction, creating a system where the total force remains balanced but movement is achieved through the reciprocal actions of the fuel and the rocket.

Rocket Propulsion

Rocket propulsion illustrates the practical application of physics in the real world. It involves a sequence of actions whereby a rocket is launched and maneuvered by the expulsion of the exhaust gases produced in the rocket engine. The underlying mechanism is the reaction force produced by the acceleration of the gas molecules.
During ignition, the rocket burns its fuel to produce high-speed gases that shoot out from the nozzles. This thrust, which is a reaction to the expulsion of the gases, propels the rocket in the opposite direction. Understanding rocket propulsion is critical to grasping how rockets are capable of traveling in the vacuum of space, where there is no air for traditional wings or propellers to push against.

Momentum in Physics

Momentum in physics is essentially the 'quantity' of motion an object possesses. It is a vector quantity, having both direction and magnitude, and is calculated as the product of an object's mass and its velocity, represented by the equation \( p = mv \).
In the context of a rocket, before ignition, both the rocket and the total mass of fuel inside it are at rest, thus the initial momentum is zero. When the rocket expels fuel at high speed, this fuel now carries momentum away from the rocket. To conserve momentum, since the system started with zero, the rocket must gain an equal momentum in the opposite direction to ensure the sum remains zero – this is what moves the rocket forward.

Closed System in Mechanics

The concept of a closed system is crucial when analyzing physical phenomena like rocket propulsion. A closed system is one in which mass is conserved within the system boundaries and no external forces are acting on it.
When contemplating the rocket and its fuel, treating this entity as a closed system simplifies the analysis by using the conservation of momentum. This system includes all the relevant masses and forces without any external influence. It allows for the prediction that the total momentum before ignition is equal to the total momentum after regardless of transformations within the system, such as the rocket burning fuel to propel itself into space. It's a key simplification that aids in understanding the fundamental operations of rockets and other similar mechanics systems.