1.) A 0.51-kg metal sphere oscillates at the end of a vertical spring. As the sp
ID: 1386434 • Letter: 1
Question
1.) A 0.51-kg metal sphere oscillates at the end of a vertical spring. As the spring stretches from 0.12 m to 0.23 m (relative to its unstrained length), the speed of the sphere decreases from 6.1 to 4.5 m/s. What is the spring constant of the spring?
2.) A spring is resting vertically on a table. A small box is dropped onto the top of the spring and compresses it. Suppose the spring has a spring constant of 500 N/m and the box has a mass of 1.3 kg. The speed of the box just before it makes contact with the spring is 0.30 m/s.
(a) Determine the magnitude of the spring
Explanation / Answer
height h = 0.23 - 0.12 = 0.11 m
By conservation of energy
m * g * h1 + 1/2 * k * x12 + 1/2 * m * v12 = 0 + 1/2 * k * x22 + 1/2 * m * v22
0.51 * 9.8 * 0.11 + 1/2 * k * 0.122 + 1/2 * 0.51 * 6.12 = 1/2 * k * 0.232 + 1/2 * 0.51 * 4.52
0.54978 + 0.0072 k + 9.48855 = 0.02645 k + 5.16375
0.01925 k = 4.87458
k = 253 N/m
------------------------------------------------------
The moment of inertia of a solid sphere = (2/5) m r2
hollow spherical shell = (2/3) m r2
Moment of inertia in this problem increases by a factor of
(5/3) (3.4)2 = 19.27
The rotation rate decreases by this same factor, and ends
2.5 / 19.27 rev/day
= 0.129 rev/day
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.