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 F_{x}= 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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