A block rests on a horizontal tabletop

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 tabletop. The horizontal force exerted on the block varies with time as follows: from

t=0\,\text{s}

t=5\,\text{s}

it increases uniformly from

0\,\text{N}

40\,\text{N}

; for

t>5\,\text{s}

it remains constant at

40\,\text{N}

. The coefficient of static friction between the block and the table is

\mu_s=0.35

and the coefficient of kinetic friction is

\mu_k=0.25

. (a) Draw and label a free-body diagram for the block while it is still at rest on the table. (b) Determine the maximum static-friction force that the surface can exert on the block. Using this value, identify every time interval during which the block is guaranteed to remain at rest, and justify your answer qualitatively and quantitatively. (c) Suppose instead that the block is already sliding to the right at

t=0\,\text{s}

. Explain how the motion of the block from

t=0\,\text{s}

t=10\,\text{s}

would differ from the situation in part (b), citing the relevant forces in your reasoning.

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