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tatuchka [14]
3 years ago
11

An astronaut living on the space station is in a constant state of free-fall- the only force exerted on her and on the space sta

tion is the gravitational force due to earth. One method of determining her mass on the space station involves vibrational motion. An astronaut sits on the chair that vibrates horizontally at the end of a spring. A motion detector determines the amplitude of vibration and the speed of the chair as it passes through the equilibrium position. The spring has a spring constant of 1200 N/m, the amplitude of vibration is 0.50 m and the speed of the chair as it passes through equilibrium is 2.0 m/s. Using these data, find the combined mass of the chair and the astronaut.
Physics
1 answer:
Radda [10]3 years ago
3 0

Answer:

m = 75 kg

Explanation:

The maximum spring potential energy will equal the maximum kinetic enrgy

½mv² = ½kx²

m = kx²/v²

m = 1200(0.50²) / 2.0²

m = 75 kg

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Work needed: 720 J

Explanation:

The work needed to stretch a spring is equal to the elastic potential energy stored in the spring when it is stretched, which is given by

E=\frac{1}{2}kx^2

where

k is the spring constant

x is the stretching of the spring from the equilibrium position

In this problem, we have

E = 90 J (work done to stretch the spring)

x = 0.2 m (stretching)

Therefore, the spring constant is

k=\frac{2E}{x^2}=\frac{2(90)}{(0.2)^2}=4500 N/m

Now we can find what is the work done to stretch the spring by an additional 0.4 m, that means to a total displacement of

x = 0.2 + 0.4 = 0.6 m

Substituting,

E'=\frac{1}{2}kx^2=\frac{1}{2}(4500)(0.6)^2=810 J

Therefore, the additional work needed is

\Delta E=E'-E=810-90=720 J

Learn more about work:

brainly.com/question/6763771

brainly.com/question/6443626

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