On your first trip to Planet X you happen to take along a 290g 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 21.1cm. You then pull the mass down 11.2cm and release it. With the stopwatch you find that 11 oscillations take 18.2s Can you now satisfy your curiosity? What is the new g?

Question

Physics

Desmond

23 September, 20:33

On your first trip to Planet X you happen to take along a 290g 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 21.1cm. You then pull the mass down 11.2cm and release it. With the stopwatch you find that 11 oscillations take 18.2s Can you now satisfy your curiosity? What is the new g?

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Answers (1)

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Lilah Summers · Answer 1

Given mass = 290g = 0.29kg Using T = 18.2/11 = 1.65s, where T = period from w = 2π/T = 3.796rad/s from w = √k/m where k = spring constant k = w²m

plugging the values,

k = (3.796) ² x 0.29 = 4.18N/m

Applying mg = kx

g = kx/m where x = 21.1cm = 0.211m g = 4.18 x 0.211/0.29 g = 3.04m/s² = the new g