Threshold of Motion

EasyPractice Problems

91.Threshold of Motion

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A stream flows over a bed of pebbles. A pebble is just barely dislodged when the drag force from the flow equals the static friction holding it down; this friction is proportional to the pebble's weight. Assume the drag force on a submerged pebble depends only on its diameter

R

, the flow speed

v

, and the water density

\rho

. A flow at

1\,\text{m/s}

just barely dislodges a pebble of diameter

1\,\text{cm}

. What flow speed just barely dislodges a pebble of diameter

4\,\text{cm}

0.25\,\text{m/s}

1\,\text{m/s}

2\,\text{m/s}

4\,\text{m/s}

16\,\text{m/s}

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