A block is attached to a horizontal spring with spring constant on a nearly…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A 0.40kg block is attached to a horizontal spring with spring constant k=50N/m on a nearly frictionless surface. A steady horizontal push of 12N is applied to the block toward the right.
A coordinate axis is chosen so that displacements to the right are positive and the equilibrium position of the undisturbed spring is x=0.
(a) After some time the block moves at constant velocity while the spring is stretched. Derive an algebraic expression for the block’s displacement xbal at which the applied push exactly balances the spring force. Your derivation must include clear reasoning about the required direction of the spring’s force relative to the chosen axis.
(b) Using your expression from part (a), compute xbal for the numerical values given.
(c) Suppose instead the positive direction were chosen to point left. Without re-deriving, state the algebraic sign that the spring force would carry at the same physical stretch and explain why the physical balance condition remains unchanged despite the sign change.