An astronaut in space cannot use a scale or balance to weigh...

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. But she does have devices to measure distance and time accurately. She knows her own mass is 78.4 $\mathrm{kg}$ , but she is unsure of the mass of a large gas canister in the airless rocket. When this canister is approaching her at 3.50 $\mathrm{m} / \mathrm{s}$ , she pushes against it, which slows it down to 1.20 $\mathrm{m} / \mathrm{s}$ (but does not reverse it) and gives her a speed of 2.40 $\mathrm{m} / \mathrm{s} .$ What is the mass of this canister?

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Key Concepts

Isolated Systems

An isolated system is one that is free from external forces or influences, making it ideal for applying conservation laws. In contexts such as space, where gravitational influences are negligible, the system can be treated as isolated, ensuring that momentum and energy conservation principles can be directly applied.

Conservation of Linear Momentum

This principle states that within an isolated system, where no external net forces are acting, the total linear momentum remains constant during interactions. It allows one to relate the velocities and masses of objects before and after they interact, which is essential for solving collision or impulse problems in mechanics.

Newton's Third Law of Motion

Newton’s Third Law states that for every action there is an equal and opposite reaction. This indicates that during an interaction, like a push or collision, the forces on both bodies are opposite in direction. This mutual interaction underpins the momentum exchange between objects, enabling the analysis of their resulting motion.

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