A vertical spring of unknown spring constant hangs from a fixed support

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

A vertical spring of unknown spring constant

k

hangs from a fixed support. A small platform of unknown mass

m

is attached to the lower end of the spring. While the system is at rest, a student pulls upward on the platform with a constant force of

2.0\,\text{N}

, causing the spring to stretch by

0.035\,\text{m}

relative to its relaxed length. The student then releases the platform; after all transients die out, the platform comes to rest once more, now

0.050\,\text{m}

below the spring’s relaxed length. Air resistance is negligible. (a) Derive expressions for the spring constant

k

and the mass

m

in terms of the known quantities

g

, the upward pulling force

F_p

, and the two measured extensions. (b) Calculate numerical values for

k

and

m

using

g = 9.8\,\text{m}\!/\!\text{s}^2

. (c) Immediately after the student stops pulling upward (that is, just after the force is removed but before any significant motion occurs), determine the magnitude and direction of the net force acting on the platform. (d) Briefly explain how your answer to part (c) is consistent with the subsequent motion that brings the platform to its final equilibrium position.

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