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. (b) Would the rocket operate in outer space where there is no atmosphere? If so, how would you steer it? Could you brake it?

Verified step by step guidance

1. Understand the principle of conservation of momentum which states that the total momentum of a closed system is constant if no external forces are acting on it. This principle applies to rockets, including in outer space.
2. Recognize that the rocket operates by expelling gas at high speed in one direction, which, according to Newton's third law (action equals reaction), propels the rocket in the opposite direction. This mechanism works in outer space despite the absence of an atmosphere.
3. Consider how to steer the rocket in outer space. Steering can be achieved by changing the direction of the expelled gas. This can be done using gimballed thrusters, which can pivot to direct their exhaust and thus change the rocket's direction.
4. Discuss the concept of braking the rocket in outer space. Braking can be achieved by expelling gas in the direction of travel, which would slow down the rocket. Alternatively, turning the rocket around and firing the main engine in the direction of travel can also act as a brake.
5. Explore additional control mechanisms such as reaction wheels or gyroscopes, which can change the orientation of the rocket without expelling mass, and are particularly useful for fine maneuvering and stabilization in space.

Key Concepts

Rocket Propulsion

Rocket propulsion is based on Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. When the rocket burns fuel and ejects gas at high speed, it generates thrust in the opposite direction, allowing it to move. This principle is crucial for understanding how rockets can operate in the vacuum of space, where there is no atmospheric pressure.

Thrust and Fuel Consumption

Thrust is the force that propels the rocket forward, generated by the expulsion of gas. The rate of fuel consumption, such as the 0.0500 kg per second mentioned, directly affects the thrust produced and the rocket's acceleration. Understanding the relationship between fuel mass, ejection velocity, and thrust is essential for analyzing the rocket's performance in space.

Steering and Braking in Space

In outer space, steering a rocket is achieved through the use of reaction control systems, which involve small thrusters that can change the rocket's orientation and trajectory. Braking is accomplished by reversing the thrust direction or using additional fuel to slow down, as there is no atmospheric drag. This requires careful planning of fuel usage and thrust management to navigate effectively in a vacuum.