Sliding-Falling Blocks

## Question:

Thank you for your encouragement. I do have a question about one of my homework problems. It is this; A system made up of two blocks, a table, a rope, and a pulley. The pulley is frictionless, and the rope is of negligible mass. Block one sits on the table and the m of friction between the block and the table is equal to .20. My question is; in order to calculate the tension on the rope does the S Fx= T-m N? Your help is greatly appreciated

## Answer:

If I understand your question correctly, we have one block sitting on a table with coefficient of kinetic friction of 0.20. A practically weightless rope is attached to the block and passed over a practically frictionless pulley at the edge of the table. A second block is suspended from the rope. If I have the setup right then the free body diagram for block one will show two vertical forces, the weight of the block downward and the reaction force from the table upward. These are equal and opposite. The horizontal forces on block one are the force of friction in one direction and the tension on the rope in the opposite direction. In this case the expression you offer, the sum of the horizontal forces equal to the difference between the friction force and the tension, is correct.

The tension in the rope will be equal to that force sufficient to overcome the frictional force on block one and to provide whatever acceleration the block is experiencing. So the mass of block one times its acceleration is one component of the tension in the rope. The mass of block one times the component of gravitational acceleration normal to the table (all of it for a horizontal table) times the coefficient of friction, is the other component of tension in the rope.

We may still be a ways from being able to calculate the number of Newtons tension in the rope. You will need to know the mass of block one to calculate the frictional force and the mass of block two, the hanging block, to calculate the acceleration of both blocks. Don't let the fact that one of the blocks moves vertically and the other horizontally confuse you. The force available to accelerate both blocks is the weight of block two minus the friction force on block one. The mass being accelerated is that of both blocks.

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JDJ