A 125 g pendulum bob hung on a string of length 35 cm has the same period as when the bob is hung from a spring and caused to oscillate. What is the spring constant?
Question
A 125 g pendulum bob hung on a string of length 35 cm has the same period as when the bob is hung from a spring and caused to oscillate. What is the spring constant?
Solution
The period of a pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
Given that the length L is 35 cm or 0.35 m and g is approximately 9.8 m/s², we can calculate the period T as follows:
T = 2π√(0.35/9.8) ≈ 1.19 s
The period of a mass-spring system is given by the formula T = 2π√(m/k), where m is the mass of the bob and k is the spring constant.
Given that the mass m is 125 g or 0.125 kg and the period T is 1.19 s, we can rearrange the formula to solve for the spring constant k:
k = m/(T/2π)² ≈ 0.125/(1.19/2π)² ≈ 3.53 N/m
So, the spring constant is approximately 3.53 N/m.
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