Astronauts and Spring question

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In summary, astronauts in space determine their mass by oscillating on a large spring attached to their belt and a wall hook. Using the equation x(t) = Acos(wt + phase constant), where A is the amplitude and w is the natural frequency, we can find the position of the astronaut at any given time. Using calculus or energy conservation, we can find the velocity of the astronaut at a specific position, such as 1.2m.
  • #1

Homework Statement




Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in the figure .

What is her mass if the spring constant is 240 ?

What is her speed when the spring's length is 1.2 ?

Homework Equations



image is http://session.masteringphysics.com/problemAsset/1001073/9/knight_Figure_14_36.jpg

The Attempt at a Solution


i got that the answer to the first question is 54.7kg

i just don't know how to find her velocity at that length
if someone can please help me
 
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  • #2
Treating the astronaut on the spring as a simple harmonic oscillator, and using the plot, can you write down the equation that represents the position (x) of the astroanut as a function of time (t) ?
 
  • #3
I would look at the natural frequency of the vibrations. This gives you the 'signature' of the system.
 
  • #4
goku do u mean x(t)=Acos(wt+phase constant)?
 
  • #5
Yes, what are the values of A and w (look at the plot)? From x(t), can you find dx/dt?

If you haven't had calculus as yet, think about energy conservation. You can find the total energy (E) using the spring constant (k) and the maximum stretch (amplitude, A). Then at x=1.2m you can plug in the value of the PE and use the value of E to find the KE at this point.
 

1. What is the connection between astronauts and spring?

The term "spring" refers to the season that occurs after winter in Earth's northern hemisphere. During this time, the Earth's tilt on its axis causes the northern hemisphere to receive more direct sunlight, resulting in warmer temperatures and longer days. This change in seasons can affect the training and schedules of astronauts, as well as the conditions of their missions.

2. How do astronauts prepare for spring during a space mission?

Astronauts undergo rigorous training to prepare for the various environmental changes they may experience during their space mission, including the transition from winter to spring. They also carefully plan their schedules and tasks to align with the changing daylight hours and weather conditions. Additionally, astronauts may bring specialized equipment and clothing to adapt to the warmer temperatures and increased sunlight.

3. What challenges do astronauts face during spring in space?

During spring, astronauts may face challenges such as adjusting to the increased sunlight and warmer temperatures, which can affect their sleep patterns and body temperature regulation. They may also encounter changes in the Earth's magnetic field and radiation levels, which can impact their health and equipment. Additionally, the changing weather conditions on Earth can affect communication with ground control and the timing of supply deliveries.

4. How does spring on Earth impact space exploration?

The changing seasons on Earth can have a significant impact on space exploration. For instance, the warmer temperatures and longer days during spring may allow for longer missions and increased productivity for astronauts. However, the potential for more severe weather systems and natural disasters during this time can also pose challenges for space missions and the safety of astronauts.

5. Are there any special events or traditions that astronauts celebrate during spring in space?

Astronauts often celebrate special occasions and holidays during their missions, including spring events such as Easter and Earth Day. They may also participate in scientific experiments and observations related to the changing seasons on Earth. Additionally, some astronauts may have personal traditions or rituals to mark the transition from winter to spring, such as taking photos of Earth or reflecting on their journey thus far.

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