On your first trip to Planet X you happen to take along a 215 g mass, a 40-cm-lo

Question

On your first trip to Planet X you happen to take along a 215 g mass, a 40-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 28.7 cm . You then pull the mass down 6.90 cm and release it. With the stopwatch you find that 10 oscillations take 16.0 s .

What is the free fall acceleration on this planet?

Explanation / Answer

time period = 2 * pi / sqrt(spring constant / mass)

10 oscillation takes 16 sec so,

1 oscillation will take 16 / 10 sec

1 oscillation will take 1.6 sec

so,

time period = 1.6 sec

mg = kx

mg = k * 0.287

k = mg / 0.287

1.6 = 2 * pi / sqrt((mass * g / 0.287) / mass)

1.6 = 2 * pi / sqrt(g / 0.287)

g = 4.4259 m/s^2

free fall accelerationm of the planet = 4.4259 m/s^2

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