On your first trip to Planet X you happen to take along a 260 g mass, a 40-cm-lo

Question

On your first trip to Planet X you happen to take along a 260 g mass, a 40-cm-long spring, a meter stick, and a stopwatch. You're curious about the acceleration due to gravity 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 30.5 cm . You then pull the mass down 8.80 cm and release it. With the stopwatch you find that 11.0 oscillations take 14.5 s .

Can you now satisfy your curiosity?

a = ?

Explanation / Answer

here,

mass = 260 g = .260 kg
length of spring = 40 cm = .4 m
Total Stretched length = 30.5 + 8.80 = 39.3 cm = 0.393m

n = 11
t = 14.5 s

Frequency of oscillatin = 11 / 14.5 = 0.75 Hz

W = 2 * pi * f
also
W = sqt(K/m)

4 * pi^2 *f^2 = K/M

k = 4 * pi^2 *f^2 *M
Where,
K is Spring Constnt
M = Mass
F = frequency of oscillations

k = 4 *3.14^ * 0.75^2 * 0.260
K = 5.76 N/m

Therefore

Spring Force = Spring Constant * Displacement
M*g = K*x

g = K*X/M
g = 5.76 * .305 / 0.260
g = 6.75 m/s^2

The acceleration due to gravity on planet X is 6.75 m/s^2

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