The Rolling Coin Separator · AI Generator #GEN-E9159EBF

Physics · mechanics

Problem

A coin sorting machine uses a clever design: coins roll down a ramp and then encounter a horizontal gap that they must jump across to reach the collection bin. The gap width is designed so that only coins of a specific radius can successfully make the jump. A quarter (radius

R = 12.3\;\text{mm}

, mass

m = 5.67\;\text{g}

) rolls without slipping down a ramp inclined at

\theta = 30°

for a distance of

d = 50\;\text{cm}

along the ramp surface. At the bottom, it launches horizontally off the edge and must clear a gap of width

w = 8.0\;\text{cm}

to land on a platform at the same height. Does the quarter successfully make the jump? Calculate the horizontal distance the quarter travels before hitting the same vertical level from which it launched.

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