Rope Pulley

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Posted on 22nd May 2006 by admin in Power Tools

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Rope Pulley
Rope Pulley
A boat is pulled into a dock by a rope attached to the bow (“front”) of the boat and passing through a pulley?

A boat is pulled into a dock by a rope attached to the bow (“front”) of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock?

Its a fixed pulley as its mentioned that pulley is at dock. So there is no mechanical advantage.
Now we can construct a triangle with 1m height and 8m base. And then calculate the angle between them.
In our case its tan-1 (1/8) = 7.125
Now we can resolve the rope speed (1m/s) along ground (along 8m base, that is the relative velocity with respect to dock)
Then speed at which boat approaching dock is 1 x cos (7.125) = 0.992 m/s
Speed will get reduced as the boat approaching dock further as the angle increasing.

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