On your first trip to Planet X you happen to take along a 180g mass, a 40-{\ m c

Question

On your first trip to Planet X you happen to take along a 180g mass, a 40-{ m cm}-long spring, a meter stick, and a stopwatch. You're curious about the free-fall acceleration on Planet X, where ordinary tasks seem easier than on earth, but you can't find this information in your Visitor's Guide. One night you suspend the spring from the ceiling in your room and hang the mass from it. You find that the mass stretches the spring by 24.0cm . You then pull the mass down 11.6cm and release it. With the stopwatch you find that 11 oscillations take 18.5s . Based on this information, what is g? ....m/s^2

Explanation / Answer

T = 2 (m/k)
T² = 4²m/k
k = 4²m/T²

On the other hand
k = mg/L

Hence
4²m/T² = mg/L
g = 4² L/T²
g = 4²×(24×10^-2)/(18.5/11)^2
g = 3.35 m/s

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