Physics

Problem

Two light, ideal springs are connected in series between a rigid ceiling support and a

0.500\,\text{kg}

block, as shown in the verbal description below. • Spring 1 (closest to the ceiling) has a known force constant of

150\,\text{N}\!\cdot\!\text{m}^{-1}

. • Spring 2 (attached to the block) has an unknown force constant

k_{2}

. • The combined system is set into small vertical oscillations. The average time for 20 complete oscillations is measured to be

34.0\,\text{s}

. Air resistance is negligible, and the springs are assumed massless. (a) Derive an expression for the effective force constant

k_{\text{eq}}

of two ideal springs connected in series. (b) Using the measured period, determine the numerical value of

k_{\text{eq}}

for the series combination. (c) Calculate the force constant

k_{2}

of Spring 2. (d) Briefly discuss whether the numerical value of

k_{2}

would be more sensitive to uncertainty in the measured period or to uncertainty in the stated value of Spring 1’s constant, and justify your answer qualitatively.

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