Question

Consider a rocket firing in the vacuum of outer space. Which of the following statements is (are) true? a) The rocket will not produce any thrust because there is no air to push against. b) The rocket will produce the same thrust in vacuum that it can produce in air. c) The rocket will produce half the thrust in vacuum that it can produce in air. d) The rocket will produce twice the thrust in vacuum that it can produce in air.

Short answer

a) A rocket needs air to generate thrust. b) A rocket will produce the same thrust in vacuum as it can in the air as long as it carries the same amount of fuel and the same power of the engine. c) A rocket will produce no thrust in vacuum since there is no air. d) A rocket will produce twice the thrust in vacuum compared to in air. Answer: b) A rocket will produce the same thrust in vacuum as it can in the air as long as it carries the same amount of fuel and the same power of the engine.

Step-by-step solution

Recall Newton's Third Law of Motion

Remember that Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This law applies to the rocket propulsion as well. When the rocket expels the combusted fuel (exhaust gases) in the backward direction, it generates an equal and opposite force in the forward direction, resulting in thrust.

Understanding Thrust in a Rocket

The thrust generated in a rocket is not directly dependent on the presence of air. Instead, it is the result of the combusted fuel (exhaust gases) being expelled at high velocities from the rocket nozzle. The momentum of the exhaust gases going out the nozzle is equal and opposite to the momentum of the rocket going forward, as per Newton's Third Law.

Comparing Statements to Understand the Rocket's Thrust in Vacuum

Now that we have a basic understanding of rocket propulsion and the generation of thrust, we will analyze each statement and compare them to our understanding. a) This statement is false, as the rocket does not need air to generate thrust. It relies on expelling exhaust gases at high velocities to create an equal and opposite force in the forward direction. b) This statement is true. A rocket will produce the same thrust in vacuum as it can in the air as long as it carries the same amount of fuel and the same power of the engine. The presence of air does not affect the thrust generated by the rocket significantly. However, it should be noted that air resistance (drag) and gravity affect the rocket's performance, which are not related to the thrust produced by the rocket. c) This statement is false, as the presence or absence of air does not significantly affect the rocket's thrust production, as explained earlier. d) This statement is also false, as the rocket does not produce twice the thrust in a vacuum compared to in air. The thrust generated by a rocket in vacuum is largely the same as that in air. Based on our analysis, only statement (b) is true.

Key concepts

Newton's Third Law of Motion

When learning about rocket thrust, especially in a vacuum, it's essential to start with one of the fundamental principles of physics: Newtons Third Law of Motion. This law states that for every action, there is an equal and opposite reaction. Imagine pushing against a wall; the wall pushes back with an equal force. This is true in space as well.

For rockets, this means that when exhaust gases are expelled in one direction, the rocket itself is pushed in the opposite direction. This basic concept underlies how rockets can move in space where there is no air. Consider a balloon; when you release the air, it flies off in the opposite direction because the air rushing out forces the balloon to move. Similarly, a rocket achieves propulsion through the expulsion of exhaust gases, creating the opposite force needed for movement.

Rocket Propulsion

The term rocket propulsion refers to the process by which a rocket moves forward. Rockets operate on the principle of thrust generation. Inside the rocket engine, fuel burns in a combustion chamber and is expelled at high speeds through a nozzle. This expulsion of exhaust gases at high speeds can create thrust because of Newton's Third Law.

Rocket propulsion in space is particularly interesting because it doesn't depend on the atmosphere. Unlike airplanes, which require air to generate lift with their wings, rockets only require propellant (fuel and oxidizer). Therefore, rockets can operate in the vacuum of space by expelling the combustion products of their fuel to move forward.

Momentum Conservation

The conservation of momentum is key to understanding how rockets can function in space where there is no air to 'push against.' When gases are expelled from the rear of the rocket, they carry momentum away from the rocket. According to the law of conservation of momentum, if no external forces are acting on a system, the total momentum of that system remains constant.

In the context of rockets, this law of physics ensures that when the momentum increases in one direction for the exhaust gases, there must be an equivalent momentum increase in the opposite direction for the rocket. This is why the absence of air does not hinder a rocket's ability to generate thrust in a vacuum; momentum is conserved whether in air or in the void of space.

Thrust Generation

Thrust generation in rockets is not about air resistance or having something to push against; it's about the high-speed expulsion of mass. The combustion process inside a rocket's engine creates enormous amounts of energy, propelling the exhaust gases in one direction and the rocket in the other due to action and reaction forces.

Interestingly, while a rocket might produce the same amount of thrust in both air and vacuum, its performance can still differ due to factors like air resistance and gravity. But these factors don't change the force produced by the rocket engines themselves. Thrust is calculated based on the mass of the exhaust gas and the velocity at which it is expelled, adhering to the equation \( Thrust = Mass_{exhaust} \times Velocity_{exhaust} \). This equation assures that rockets can create the necessary thrust for lift-off and maneuvering in space, entirely independent of the presence of an atmospheric medium.