Physics

Problem

Block

C

(

2.0\,\text{kg}

) rests on top of block

D

(

4.0\,\text{kg}

), which in turn slides on a horizontal floor. The coefficient of static friction between

C

and

D

\mu_{s}=0.50

, while the coefficient of kinetic friction between

D

and the floor is

\mu_{k}=0.20

. A horizontal force of

25\,\text{N}

is applied to block

D

toward the right. What is the acceleration of block

C

? (Take

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

.) a)

4.3\,\text{m/s}^2

to the right b)

2.9\,\text{m/s}^2

to the right c)

2.2\,\text{m/s}^2

to the right d)

1.3\,\text{m/s}^2

to the right

Intuitive explanation

The key is to first determine whether blocks $C$ and $D$ move together or slip relative to each other. Find the maximum static friction force that can act on $C$ , then assume they accelerate as one system and check if that friction demand exceeds the limit. If it does, $C$ and $D$ slip, and $C$ accelerates only under the friction force the floor can actually provide through $D$ .

Intuitive explanation

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