Chapter 8: Problem 61
A 70-kg astronaut floating in space in a 110-kg MMU (manned maneuvering unit) experiences an acceleration of 0.029 m/s\(^2\) when he fires one of the MMU's thrusters. (a) If the speed of the escaping N\(_2\) gas relative to the astronaut is 490 m/s, how much gas is used by the thruster in 5.0 s? (b) What is the thrust of the thruster?
Short Answer
Step by step solution
Determine the Total Mass
Calculate the Thrust (Force) Produced by the Thruster
Find the Mass Flow Rate of Escaping Gas
Calculate the Total Mass of Gas Used in 5 Seconds
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Newton's Second Law
\[ F = ma \]
where:
- \( F \) is the force (in newtons, N),
- \( m \) is the mass of the object (in kilograms, kg),
- \( a \) is the acceleration (in meters per second squared, m/s²).
Understanding how this law works is crucial in many applications, from calculating weaponry trajectories to designing space vehicles.
Thrust Calculation
\[ F = ma \]
where:
- \( F \) is the thrust or force exerted by the thruster,
- \( m \) is the total mass of the system being accelerated (in this case, the astronaut and the MMU),
- \( a \) is the acceleration provided by the thruster.
Mass Flow Rate
The relationship is given by the equation:
\[ F = \dot{m} \times v \]
where:
- \( F \) is thrust,
- \( \dot{m} \) is the mass flow rate (in kilograms per second, kg/s),
- \( v \) is the exhaust velocity (in meters per second, m/s).
Rocket Propulsion
Understanding rocket propulsion helps bridge the gap between theoretical physics and practical engineering, guiding the design of efficient spacecraft.
Kinematics
Kinematic equations can be further used to determine position and velocity at any given time, making them indispensable for planning and executing maneuvers in aerospace applications.