Two ideal massless springs with force constants and are connected in series between a…

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

Problem

Two ideal massless springs with force constants

k_1=100\,\text{N}\!\cdot\!\text{m}^{-1}

and

k_2=200\,\text{N}\!\cdot\!\text{m}^{-1}

are connected in series between a rigid wall and a

0.50\,\text{kg}

cart on a horizontal, frictionless track. The cart is pulled away from the wall so that the total extension of the spring pair is

x_{\text{tot}}=0.20\,\text{m}

and then held at rest. (a) Determine the equivalent single-spring constant

k_{\text{eq}}

for the two-spring combination. (b) Using your result from part (a), calculate the total elastic potential energy stored in the two springs at the given extension.

Related theory

Potential Energy
Common Forces in Mechanics
Work done on a spring and elastic potential energy
Work, Energy and Power
Potential energy of a spring

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