Astronauts in space cannot weigh themselves by standing on a bathroom scale. Ins

Question

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 (Figure 1). Part A What is her mass if the spring constant is 310 N/m? Express your answer to two significant figures and include m = 71 kg Part B What is her speed when the spring's length is 0.90 m? Express your answer to two significant figures and include the v = 0.8369 m/s

Explanation / Answer

from the graph,

Length of the spring, Lo = 1 m

Amplitude = 0.4 m

Time period, T = 3 s

A) angular frequency, w = 2*pi/T

= 2*pi/3

= 2.094 rad/s

we know, angular frequency, w = sqrt(k/m)

w^2 = k/m

==> m = k/w^2

= 310/2.094^2

= 70.7 kg

= 71 kg (when rounder to two singinificant figures)

b) when L = 0.9 m

compression of the spring, x = 1 - 0.9

= 0.1 m

Apply conservation of energy

(1/2)*m*v^2 + (1/2)*k*x^2 = (1/2)*k*A^2

m*v^2 = k*A^2 - k*x^2

v^2 = k*A^2/m - x^2

v = sqrt(k*A^2/m - x^2)

= sqrt(310*0.4^2/70.7 - 0.1^2)

= 0.83 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.