A 100.0 g mass is hung from a spring. A measurement is taken by using a ruler pl

Question

A 100.0 g mass is hung from a spring. A measurement is taken by using a ruler placed next to the spring to measure the position of the bottom of the mass carrier. This reads 55.0 cm. A additional mass of 46.0 g is added to the spring (the stripy rectangle in the second part of the diagram). The position of the end of the spring is now measured to be 61.6 cm 10 cm 10 cm ruler ruler 100 cm 100 cm What is the spring constant for this spring? Nm-1 Check Another mass of 31.0 g is added to the spring. What is the reading on the ruler now? cm Check

Explanation / Answer

Here ,

part a) let the spring constant is k

when an additional 46 gm mass is attached to the spring

change in reading = 0.616 - 0.55 = 0.066 m

Now, as

k * x = m * g

k * 0.066 = 0.046 * 9.8

k = 6.83 N/m

the spring constant is 6.83 N/m

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if 31 gm is added

extra extension in spring = m * g/k

extra extension in spring = 0.031 * 9.8/6.83

extra extension in spring =0.045 m = 4.5 cm

new reading = 61.1 + 4.5 = 65.6 cm

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as the motion will be simple harmonic

frequency = 1/(2pi) * sqrt(k/total mass)

frequency = 1/(2pi) * sqrt(6.83/(0.100 + 0.046 + 0.031))

frequency = 0.99 Hz

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