Normal Force of a Sliding Rope: Debunking the Myth

[PatPwnt]

If I have an extended (uncoiled) rope sitting on a table, and part of it is hanging off the edge of the table so that it starts to slide (there is friction), how would the normal force of the table acting on the rope change as it slides off? This has been bugging me for weeks, because people keep telling me that the normal force is just the weight of the rope on top of the table. I have a hard time believing this because the rope hanging over the edge may still pull the table top rope, contributing to the normal force.

 

[rcgldr]

Assuming an idealized case where dynamic coefficient of friction is constant regardless of speed, the friction force = (weight of rope on table) x (dynamic coefficient of friction). The downwards force beyond the edge of the table = weight of segment of rope between edge of table and ground.

 

[PatPwnt]

The downwards force beyond the edge of the table still tugs on the part of the rope on the table though. So the normal force must also cancel this out and may be different than just the weight of the rope on the table.

 

[rcgldr]

There's no rule that states the forces cancel. Assuming the downwards force is greater than the friction force, then the rope accelerates.

 

[PatPwnt]

I mean that the part of the rope on top of the table stays on the table until it moves over the edge. If the rope isn't moving upward off the table or downward through the table, then the forces must be canceling. That's the rule. So why would the normal force only be the weight of the rope on top of the table when the rope hanging over is still pulling down on it?

 

[rcgldr]

I mean that the part of the rope on top of the table stays on the table until it moves over the edge. If the rope isn't moving upward off the table or downward through the table, then the forces must be canceling. That's the rule. So why would the normal force only be the weight of the rope on top of the table when the rope hanging over is still pulling down on it?

Think of the edge of the table as a frictionless, intertialess pulley, the downforce from the rope on the outer part of the pulley is converted into a sideforce on the inner part of the pulley.

 

[PatPwnt]

But, that is not what is happening. If we consider there to be a pulley. It must be considered part of the system. Then the rope pulling down on the side also pulls down on the pulley and it also has a normal force.

 

[rcgldr]

But, that is not what is happening. If we consider there to be a pulley. It must be considered part of the system. Then the rope pulling down on the side also pulls down on the pulley and it also has a normal force.

The end of the table or whatever the pulley is mounted to reacts to any downwards component of force by deforming (compressing) a tiny amount and exerting an opposing upwards force.