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. Supppose 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 Figure P14.36. Figure P14.36

(a) What is her mass if the spring constant is 220 N/m? kg (b) What is her speed when the spring's length is 0.80 m? m/s

Explanation / Answer

(a)
k = 220 N/m
From graph it is pretty clear, time period t = 3.0 s
We know,
t =  2**sqrt(m/k)
3.0 = 2**sqrt(m/220)
m = 50.15 Kg

(b)
Amplitue, A = 0.4 m
Total Energy = 1/2*k*A^2

At L = 0.8 m,

Total Energy = 1/2*k*x^2 + 1/2*m*v^2

Using Energy Conservation,
1/2*k*A^2 = 1/2*k*x^2 + 1/2*m*v^2
220 * 0.4^2 = 220 * 0.2^2 + 50.15 * v^2
v = 0.725 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.