Chapter 3: Problem 4

An astronaut working with many tools some distance away from a spacecraft is stranded when the "maneuvering unit" malfunctions. How can the astronaut return to the spacecraft by sacrificing some of the tools?

Short Answer

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Answer: An astronaut can use the law of conservation of momentum by throwing one or more tools in the opposite direction of the spacecraft. This will create an equal and opposite momentum, according to Newton's third law, which will propel the astronaut back towards the spacecraft. The astronaut needs to calculate the required momentum and choose appropriate tools to generate the necessary change in momentum for a successful return.

Step by step solution

Understand the law of conservation of momentum

The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces are acting upon it. In this situation, the astronaut and the tools form a closed system, and the only way to create a change in momentum is by "sacrificing" some of the tools.

Isolate the action and reaction pair

The astronaut will need to create a change in momentum by throwing one or more tools in the direction opposite to the spacecraft, according to Newton's third law of motion. This states that for every action, there is an equal and opposite reaction. By throwing a tool with a certain momentum, the astronaut will create an equal and opposite momentum that will propel them back towards the spacecraft.

Calculate the required momentum

To calculate the required momentum to get back to the spacecraft, we need to consider the astronaut's mass (m_a), the tool's mass (m_t), and the desired velocity (v) of the astronaut towards the spacecraft (assuming the initial velocity of the astronaut is zero). The equation for momentum is: momentum = mass × velocity The astronaut's final momentum (p_a) should be equal and opposite to the tool's momentum (p_t). So, p_a = -p_t

Choose an appropriate tool or set of tools

Now that the conservation of momentum principle is understood, the astronaut needs to choose a tool or set of tools that, when thrown, will provide the necessary change in momentum. This can be done by analyzing the mass and velocity of the tools available and selecting the ones that would be the most effective in achieving the desired result. The astronaut may need to use multiple tools, thrown consecutively or simultaneously, to generate the required momentum.

Execute the plan

Once the astronaut has chosen the tool(s), they need to execute their plan. They should ensure that they are in a stable position and throw the tool(s) firmly in the opposite direction of the spacecraft. This action will generate a reaction force that will propel the astronaut towards the spacecraft, allowing them to return safely.

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An astronaut working with many tools some distance away from a spacecraft is stranded when the "maneuvering unit" malfunctions. How can the astronaut return to the spacecraft by sacrificing some of the tools?

Short Answer

Step by step solution

Understand the law of conservation of momentum

Isolate the action and reaction pair

Calculate the required momentum

Choose an appropriate tool or set of tools

Execute the plan

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