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

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In the pulley system described, a 1kg mass on a table is connected to a 3kg mass hanging off the edge, with a frictional resistance of 0.5 N acting on the 1kg mass. When released, the system experiences friction that affects the total work done. The expected work done by friction, calculated as the product of the frictional force and the distance moved, is initially thought to be 0.25 J. However, the correct total work done by friction is determined to be 3.8625 J, indicating a more complex interaction in the system. Understanding the impact of friction in such scenarios is crucial for accurate calculations in physics.
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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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