Question

A small rocket burns 0.0500 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1600 m/s. (a) What is the thrust of the rocket? (b) Would the rocket operate in outer space where there is no atmosphere? If so, how would you steer it? Could you brake it?

Short answer

(a) Thrust is 80 N. (b) Yes, it operates in space. Steering is possible by adjusting thrust direction; braking via a retro-burn.

Step-by-step solution

Understand Thrust Formula

Thrust is the force exerted by the rocket's engine as it expels gas. The formula for thrust ( \( F \) ) is given by: \[ F = \dot{m} \cdot v_e \] where \( \dot{m} \) is the mass flow rate of fuel and \( v_e \) is the relative velocity of the exhaust gas.

Identify Given Values

From the information given: - The mass flow rate of fuel, \( \dot{m} = 0.0500 \ \text{kg/s} \). - The relative velocity of the exhaust, \( v_e = 1600 \ \text{m/s} \).

Calculate the Thrust

Using the thrust formula: \[ F = \dot{m} \cdot v_e \] Substitute the given values: \[ F = 0.0500 \ \text{kg/s} \cdot 1600 \ \text{m/s} = 80 \ \text{N} \] Thus, the thrust of the rocket is 80 N.

Determine Rocket Operation in Outer Space

Rockets can operate in outer space because they rely on the expulsion of gases for thrust, not on air around them. The thrust depends solely on the mass flow rate and the velocity of the expelled gas.

Exploring Steering and Braking

Steering in space can be achieved by adjusting the direction of the exhaust gas ejection, using fins, gimballed engines, or directional nozzles. Braking can be performed by reversing the thrust direction, for example, by turning the rocket around and firing the engines, which is often referred to as a retro-burn.

Key concepts

Mass Flow Rate

The mass flow rate is a fundamental concept in rocket propulsion. It represents the amount of mass being expelled from the rocket per unit of time. In simpler terms, it tells us how fast the fuel is being used and turned into exhaust gas.
The mass flow rate has a direct impact on the thrust a rocket can generate. This is because the higher the mass flow rate, the more mass there is to accelerate, thus increasing the force exerted by the rocket. It is typically measured in kilograms per second (kg/s).

• In our example, the mass flow rate is 0.0500 kg/s.
• This means that 0.0500 kg of fuel is burnt and ejected as exhaust every second.

An intuitive way to understand this is by comparing it to a garden hose. The more water flows out of the hose per second, the stronger the water pressure felt on your hand.​

Exhaust Velocity

The exhaust velocity is another crucial aspect of rocket propulsion. It indicates the speed at which the exhaust gases are expelled from the rocket. This speed is relative to the rocket itself.
Think of the exhaust velocity as how fast the rocket pushes back against the ejected gases. The faster the gases are expelled, the greater the force on the rocket in the opposite direction. This principle is defined by Newton's third law: for every action, there is an equal and opposite reaction.

• In the given problem, the exhaust velocity is 1600 m/s.
• This means the gases are pushed out at a speed of 1600 meters every second.

High exhaust velocity is essential for achieving efficient rocket thrust and is influenced by the engine design and the type of propellant used.

Rocket Propulsion

Rocket propulsion is a fascinating area of physics that enables rockets to travel through the atmosphere and beyond. It involves converting chemical energy from the rocket fuel into kinetic energy of the expelled gases, creating thrust.
The entire process can be broken down as follows:

• Fuel is burnt in the rocket’s engine, creating hot gases.
• The gases expand and are expelled through the rocket’s nozzle at high speeds.
• The expulsion of gases generates an upward force, or thrust, that propels the rocket forward.

This mechanism is why rockets do not require air to generate thrust. They carry both fuel and an oxidizer needed for combustion. Therefore, the rocket engine works efficiently even in the vacuum of space.

Thrust in Outer Space

One of the wonders of rocket science is how rockets can operate in the vacuum environment of outer space. Unlike jet engines, rockets do not rely on atmospheric oxygen. They can produce thrust by expelling the gases generated from burning fuel.
In outer space, thrust generation relies solely on the mass flow rate and the exhaust velocity. No external air or atmospheric pressure is necessary.

• The thrust continues to propel the rocket forward based on the internal expulsion of gases.
• Maneuvering and steering are achieved by altering the direction of the expelled gases.

Even in the absence of air resistance or upthrust, rockets can steer through space by adjusting their nozzles or engines. Slowing down, or braking, involves reversing the direction of thrust, often by turning the rocket and firing its engines in the opposite direction, a procedure known as retro-burning.