Solve Mass Using Spring & Oscillation

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SUMMARY

The discussion focuses on calculating an astronaut's mass using a spring oscillation method in a microgravity environment. The spring constant is specified as 240 N/m, and the astronaut's displacement from equilibrium is determined to be 0.8 m. The user initially calculates the force exerted by the spring as 208 N and subsequently derives the mass as approximately 21.22 kg using the equation m = F/g, where g is the acceleration due to gravity (9.8 m/s²). The user expresses uncertainty about their approach and seeks clarification on the correctness of their calculations.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Knowledge of gravitational force and mass relationship (mg = weight)
  • Familiarity with oscillatory motion principles
  • Basic algebra for solving equations
NEXT STEPS
  • Review the principles of oscillation and spring dynamics
  • Learn about the derivation and application of Hooke's Law
  • Study the effects of microgravity on mass measurement techniques
  • Explore advanced topics in dynamics related to oscillatory systems
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding mass measurement techniques in microgravity environments, particularly in the context of space missions.

azn4life1990
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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

http://session.masteringphysics.com/problemAsset/1073872/3/knight_Figure_14_36.jpg
What is her mass if the spring constant is 240N/m

Homework Equations



Hookes Law
F = -kx
U = (1/2)*k*x2

The Attempt at a Solution



So the spring was pulled back 1.4 metres and then released where it went to the point 0.6
so 0.6 is the point at equilibrium, so -0.8 is the displacement and that is the x

F = (240 * 0.8)
and then I am not sure what to do, I am not even sure if I am doing this right and help would be appreciated
 
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im pretty sure my approach is wrong...

F = -260 * -0.8 = 208N

mg = weight

208/9.8 = m

m = 21.224489795918367346938775510204kg

im sure that's wrong is there a better way to approach this problem and why is the way I am approaching it wrong?
 

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