A block rests on a rough horizontal floor

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

Problem

10\,\text{kg}

block rests on a rough horizontal floor. A time-dependent horizontal force

F(t) = k t

is applied, where

k = 6\,\text{N\,s}^{-1}

and

t

is in seconds. The coefficients of friction between the block and the floor are

\mu_s = 0.40

and

\mu_k = 0.35

. Take

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

. Respond to the following. (i) Calculate the maximum static friction that can act on the block. (ii) Determine the time

t_0

at which the block just begins to move. (iii) Write an expression for the net horizontal force acting on the block for

t > t_0

. (iv) Derive the acceleration of the block as a function of time

a(t)

for

t > t_0

. (v) Compute the acceleration at

t = 8\,\text{s}