A block rests on a horizontal surface

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

Problem

2.0\,\text{kg}

block rests on a horizontal surface. The block is attached to an ideal spring of spring constant

50\,\text{N}\!/\!\text{m}

that is fixed to a wall. The coefficient of kinetic friction between the block and the surface is

\mu_k = 0.20

. The spring is compressed

0.25\,\text{m}

and the block is held in place. At

t=0

the block is released and begins sliding toward the right. (a) Draw a clearly labeled free-body diagram for the block at the instant it is

0.10\,\text{m}

from the equilibrium position and moving rightward. (b) Derive an algebraic expression for the block’s instantaneous acceleration at that location in terms of

k

m

\mu_k

g

, and

x

, where

x

is the block’s displacement from equilibrium (take

x>0

to the right). (c) Calculate the numerical value (with sign) of the acceleration when

x = +0.10\,\text{m}

. (d) State whether the block is speeding up or slowing down at that instant and justify your answer using the sign of the net force and the block’s velocity direction.

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