Astronaut Spacewalk Force Calculation A Physics Problem

Introduction

In the vast expanse of space, astronauts often undertake spacewalks, venturing outside the confines of their spacecraft to perform critical tasks such as repairs, maintenance, and scientific experiments. These spacewalks present unique challenges, as astronauts must contend with the absence of gravity and the need to maneuver themselves effectively in the weightless environment. Understanding the physics principles governing motion in space is crucial for ensuring the safety and success of these missions.

One fundamental aspect of spacewalks is the application of Newton's laws of motion. These laws dictate how objects move and interact with each other, providing the foundation for understanding the astronaut's movements in space. This article delves into a fascinating scenario involving a 63 kg astronaut embarking on a spacewalk. Starting from rest, the astronaut pushes off the shuttle with a velocity of 1.2 m/s, propelling themselves to a different location outside the spacecraft. Our objective is to determine the astronaut's force with respect to the shuttle after 3 seconds. This exploration will not only illuminate the practical application of physics principles in space but also highlight the intricate calculations involved in ensuring the astronaut's controlled movement and safety during a spacewalk.

Problem Statement

Consider a scenario where a 63 kg astronaut is on a spacewalk, initially at rest relative to the shuttle. The astronaut pushes off the shuttle with a velocity of 1.2 m/s, propelling themselves to a different location outside the spacecraft. We aim to determine the astronaut's force with respect to the shuttle after 3 seconds. This problem involves applying the principles of Newton's laws of motion, particularly the concepts of impulse and momentum, to calculate the force exerted by the astronaut during the push-off. Understanding this force is crucial for ensuring the astronaut's controlled movement and safety during the spacewalk.

Key Information:

• Astronaut's mass (m) = 63 kg
• Astronaut's initial velocity (v₀) = 0 m/s (at rest)
• Astronaut's final velocity (v) = 1.2 m/s
• Time duration (t) = 3 seconds

Objective:

Calculate the astronaut's force (F) with respect to the shuttle after 3 seconds.

Theoretical Background

To solve this problem, we will utilize the following physics principles:

1. Newton's Second Law of Motion: This law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
2. Impulse-Momentum Theorem: This theorem states that the impulse acting on an object is equal to the change in momentum of the object (J = Δp). Impulse is defined as the force acting on an object multiplied by the time interval over which it acts (J = Ft), and momentum is defined as the mass of an object multiplied by its velocity (p = mv).
3. Relationship between Impulse and Momentum: Combining the Impulse-Momentum Theorem, we get Ft = Δp = m(v - v₀), where:
   • F is the force
   • t is the time interval
   • m is the mass
   • v is the final velocity
   • v₀ is the initial velocity

By applying these principles, we can determine the force exerted by the astronaut during the push-off from the shuttle. Understanding these fundamental concepts is critical for accurately calculating the forces involved in spacewalks and ensuring the safety of astronauts.

Calculation Steps

To determine the astronaut's force with respect to the shuttle, we will follow these steps:

1. Calculate the change in momentum (Δp):
   • Δp = m(v - v₀)
   • Where:
     • m = 63 kg (astronaut's mass)
     • v = 1.2 m/s (final velocity)
     • v₀ = 0 m/s (initial velocity)
   • Δp = 63 kg * (1.2 m/s - 0 m/s) = 63 kg * 1.2 m/s = 75.6 kg⋅m/s

The change in momentum represents the difference between the astronaut's final and initial states of motion. This value is crucial for understanding the impact of the push-off on the astronaut's movement.

2. Apply the Impulse-Momentum Theorem (Ft = Δp):
   • We know that the impulse (Ft) is equal to the change in momentum (Δp).
   • We have calculated Δp as 75.6 kg⋅m/s.
   • We are given the time interval (t) as 3 seconds.
   • Therefore, Ft = 75.6 kg⋅m/s.

This step connects the change in momentum to the force exerted over the specified time interval. It sets the stage for calculating the force itself.

3. Solve for the force (F):
   • F = Δp / t
   • F = 75.6 kg⋅m/s / 3 s
   • F = 25.2 N

This calculation yields the magnitude of the force exerted by the astronaut. The resulting force value is essential for understanding the physical interaction between the astronaut and the shuttle.

Therefore, the astronaut's force with respect to the shuttle after 3 seconds is 25.2 N. This force propelled the astronaut away from the shuttle, initiating their spacewalk. The calculated force provides a quantitative understanding of the interaction between the astronaut and the shuttle, highlighting the practical application of physics principles in space travel.

Detailed Explanation of the Solution

In this section, we provide a more in-depth explanation of the solution, clarifying the physics concepts and their application to the problem. The problem at hand involves an astronaut of mass 63 kg, initially at rest, pushing off the shuttle with a final velocity of 1.2 m/s. Our goal is to find the force exerted by the astronaut with respect to the shuttle after 3 seconds.

Step 1: Calculating the Change in Momentum (Δp)

The first step in solving this problem is to calculate the change in momentum (Δp) of the astronaut. Momentum, denoted as p, is a measure of an object's mass in motion and is calculated as the product of mass (m) and velocity (v). The change in momentum (Δp) is the difference between the final momentum (mv) and the initial momentum (mv₀). Mathematically, this is represented as:

Δp = m(v - v₀)

In this case, the astronaut's mass (m) is 63 kg, the final velocity (v) is 1.2 m/s, and the initial velocity (v₀) is 0 m/s (since the astronaut starts from rest). Plugging these values into the equation, we get:

Δp = 63 kg * (1.2 m/s - 0 m/s) = 63 kg * 1.2 m/s = 75.6 kg⋅m/s

The change in momentum (Δp) is 75.6 kg⋅m/s. This value represents the amount of momentum the astronaut gained as a result of pushing off the shuttle. It is a crucial intermediate step in determining the force exerted.

Step 2: Applying the Impulse-Momentum Theorem (Ft = Δp)

The next crucial step is applying the Impulse-Momentum Theorem, which relates the impulse acting on an object to the change in its momentum. Impulse (J) is defined as the product of the force (F) acting on an object and the time interval (t) over which it acts. The Impulse-Momentum Theorem states that the impulse (J) is equal to the change in momentum (Δp). Mathematically, this is represented as:

Ft = Δp

Here, F is the force exerted, t is the time interval, and Δp is the change in momentum. We have already calculated the change in momentum (Δp) as 75.6 kg⋅m/s. The problem states that the time interval (t) is 3 seconds. Thus, we can set up the equation as:

Ft = 75.6 kg⋅m/s

This equation provides a direct link between the force exerted by the astronaut and the change in their momentum over the specified time interval. It sets the stage for solving for the force.

Step 3: Solving for the Force (F)

Now that we have the equation Ft = 75.6 kg⋅m/s, we can solve for the force (F). To do this, we divide both sides of the equation by the time interval (t), which is 3 seconds:

F = Δp / t

Substituting the values, we get:

F = 75.6 kg⋅m/s / 3 s

Performing the division, we find:

F = 25.2 N

Therefore, the force exerted by the astronaut with respect to the shuttle after 3 seconds is 25.2 N. This calculated force represents the average force the astronaut exerted during the push-off. The positive value indicates that the force is in the direction of the astronaut's motion away from the shuttle.

Summary of the Solution

In summary, we calculated the force exerted by the astronaut by first finding the change in momentum (Δp), which is 75.6 kg⋅m/s. We then applied the Impulse-Momentum Theorem (Ft = Δp) and solved for the force (F), which is 25.2 N. This force allowed the astronaut to move away from the shuttle at a velocity of 1.2 m/s. The detailed explanation clarifies the physics principles involved and their application to this specific problem.

Real-World Applications and Implications

The principles and calculations discussed in this article have significant real-world applications and implications, particularly in the context of space exploration and astronaut safety. Understanding the forces involved in spacewalks is crucial for designing safe and effective procedures for astronauts working outside spacecraft. The application of Newton's laws of motion and the Impulse-Momentum Theorem allows engineers and mission planners to accurately predict and control the movements of astronauts in the weightless environment of space. This knowledge is essential for tasks such as:

1. Maneuvering in Space: Astronauts often need to move from one location to another outside the spacecraft, whether to perform repairs, conduct experiments, or install equipment. By understanding the relationship between force, mass, and acceleration, astronauts can use controlled pushes and pulls to navigate effectively. The calculations we performed in this article help illustrate how a specific force applied over a certain time interval results in a change in momentum, allowing astronauts to move in a predictable manner. This precise control is vital for maintaining orientation and avoiding collisions with the spacecraft or other objects.

2. Maintaining Stability: When performing tasks in space, astronauts need to maintain stability to ensure accurate and safe operations. Applying Newton's Third Law of Motion (for every action, there is an equal and opposite reaction), astronauts must be mindful of the forces they exert. For example, tightening a bolt requires applying a force, which in turn exerts an equal and opposite force on the astronaut. Without proper bracing or stabilization, this reaction force could cause the astronaut to drift away. Understanding these interactions allows astronauts to use tethers, foot restraints, and handholds to stabilize themselves while working.

3. Emergency Procedures: In the event of an emergency, such as a detached tether or a loss of propulsion, astronauts need to be able to use their knowledge of physics to regain control and return to the spacecraft safely. Calculating the necessary force and direction to propel themselves back to the shuttle is crucial. The principles discussed in this article provide the foundation for such calculations. Training simulations and emergency protocols are designed to prepare astronauts for these scenarios, ensuring they can apply these principles under pressure.

4. Spacecraft Design: The design of spacecraft and spacesuits also relies heavily on understanding the forces involved in spacewalks. Spacesuits are designed to provide astronauts with the necessary mobility and protection while minimizing the effort required to move. Spacecraft are equipped with handholds, foot restraints, and other devices to aid astronauts in maneuvering and maintaining stability. The calculations and principles discussed here inform these design considerations, optimizing the functionality and safety of equipment used in space.

5. Mission Planning: Planning a spacewalk involves careful consideration of the tasks to be performed, the tools and equipment required, and the movements the astronaut will need to make. Understanding the physics of motion in space allows mission planners to estimate the time and resources required for each task, ensuring the mission is completed efficiently and safely. This includes accounting for the astronaut's mass, the forces they will exert, and the time it will take to move between locations.

6. Training and Simulation: Astronauts undergo extensive training to prepare for spacewalks, including simulations in underwater environments or on partial gravity simulators. These simulations allow astronauts to practice maneuvering, using tools, and responding to emergencies in a controlled setting. The principles and calculations discussed in this article are integral to these training programs, ensuring astronauts have a solid understanding of the physics governing their movements in space.

In conclusion, the principles and calculations demonstrated in this article are not just theoretical exercises; they are fundamental to the practical aspects of space exploration and astronaut safety. The ability to accurately predict and control movement in space is crucial for the success of missions and the well-being of astronauts. As space exploration continues to advance, a deep understanding of these principles will remain essential for future endeavors.

Conclusion

In this article, we have explored a fundamental problem in space physics: calculating the force exerted by an astronaut during a spacewalk. We considered a scenario involving a 63 kg astronaut pushing off the shuttle with a velocity of 1.2 m/s and calculated the force with respect to the shuttle after 3 seconds. By applying Newton's laws of motion and the Impulse-Momentum Theorem, we determined that the astronaut exerted a force of 25.2 N. This calculation not only provides a quantitative understanding of the interaction between the astronaut and the shuttle but also highlights the practical application of physics principles in space travel.

The detailed explanation of the solution underscored the importance of understanding the concepts of momentum and impulse. The change in momentum, calculated as 75.6 kg⋅m/s, represented the astronaut's gain in motion due to the push-off. The Impulse-Momentum Theorem then allowed us to connect this change in momentum to the force exerted over a specific time interval. Solving for the force, we arrived at 25.2 N, which is the average force the astronaut exerted during the 3-second interval. This force enabled the astronaut to move away from the shuttle at the desired velocity.

Furthermore, we discussed the real-world applications and implications of these principles in the context of space exploration. Understanding the forces involved in spacewalks is crucial for ensuring astronaut safety and mission success. From maneuvering in space to maintaining stability, from emergency procedures to spacecraft design, and from mission planning to training and simulation, the principles discussed here are integral to various aspects of space travel. Astronauts rely on these principles to navigate effectively, stabilize themselves while working, and respond to emergencies. Spacecraft and spacesuit designs are also informed by these calculations, optimizing functionality and safety. Mission planners use these principles to estimate time and resources, while training programs incorporate them to prepare astronauts for the challenges of spacewalks.

In summary, the ability to accurately calculate and understand forces in space is essential for the continued advancement of space exploration. The principles and calculations explored in this article provide a foundational understanding of the physics governing movement in the weightless environment of space. As we continue to venture further into the cosmos, a deep appreciation of these principles will remain critical for ensuring the safety and success of future missions. The exploration of space demands a rigorous application of physics, and this example demonstrates just one facet of the complex interplay between theory and practice in this exciting field.