physics
A bicycle chain is wrapped around a rear sprocket (r = 0.039m) and a front sprocket (r = 0.10m). The chain moves with a speed of 1.4m/s around the sprockets, while the bike moves at a constant velocity. Find the magnitude of the acceleration of a chainlink that is in contact with (a) the rear sprocket, (b) neither sprocket, and (c) the front sprocket.
How do I set this up to get the answers?
You are given tangential velocity. On the sprockets, acceleration is tangential velocity squared divided by radius.
You are given tangential velocity. On the sprockets, acceleration is tangential velocity squared divided by radius.
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Answers
The acceleration of a chainlink at a point is the change in its tangential velocity over time. Since the chain is moving at a constant velocity around the sprockets, its tangential velocity will remain constant. Thus, the acceleration of a chainlink in contact with either sprocket is the tangential velocity squared (1.4 m/s2) divided by the radius of the sprocket. For the chainlink in contact with the rear sprocket, its acceleration will be 1.4 m/s2 / 0.039 m = 35.90 m/s2. For the chainlink in contact with the front sprocket, its acceleration will be 1.4 m/s2 / 0.10 m = 14.00 m/s2. For the chainlink in contact with neither sprocket, its acceleration will be zero.
