On your first trip to Planet X you happen to take along a 110 g mass, a 40 - c m

Question

On your first trip to Planet X you happen to take along a 110gmass, 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 29.1cm . You then pull the mass down 10.9cmand release it. With the stopwatch you find that 11 oscillations take 18.2s

Can you satisfy your curiosity?

Explanation / Answer

f=kx for a spring, where f is force applied, x distance extended and k is spring constant

so, 0.110*g=0.291*k => k=0.37*g------(1)

now frequency w=sqrt(k/m)

w=2*pi*frequency=2*pi*0.604=3.797

therefore,

3.797=sqrt(0.37*g/0.11)

14.41=0.37*g/0.11

=>g=4.286m/s^2

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