How Does Friction Affect Work in a Pulley System with Unequal Masses?

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The discussion focuses on calculating the total work done by friction in a pulley system involving a 1kg mass on a table and a 3kg mass hanging vertically. The frictional resistance is specified as 0.5 N, and the 1kg mass does not reach the pulley, stopping before it can do so. The correct total work done by the frictional force is determined to be 3.8625 J, which contrasts with the initial assumption that it would be 0.25 J based on the distance moved and the frictional force.

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A mass of 1kg rests on a horizontal table. It is connected by a taut, light, inextensible string passing over a smooth fixed pulley, at the edge of the table, to another mass of 3kg hanging vertically. The 3kg mass it at a height of 0.5 metres above an inelastic floor when the system is released from rest. There is also a frictional resistance to the motion from the table of 0.5 N. Determine the total work done by the frictional force, assuming that the 1kg mass stop before reaching the pulley.


I've included a diagram I drew. I am not quite sure where to go with this question. Could you help me out?

The answer I'm looking for is 3.8625 J.
 

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This question is strange. I would think that if the frictional force is 0.5N and the box moved 0.5m, the work done by friction would be 0.25J.
 

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