Tension of rod connecting two cylinders

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Homework Help Overview

The problem involves two cylinders of equal mass, one hollow and one solid, connected by a light rod and placed on an inclined plane. The task is to find the tension in the rod as the system rolls down the incline without skidding. The discussion revolves around the factors contributing to the tension in the rod and the dynamics of the system.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the origins of tension in the rod, questioning whether it arises from the difference in altitudes of the cylinders or from their differing moments of inertia. Some suggest that the tension may not be constant and could depend on time.

Discussion Status

The discussion is active, with participants sharing various perspectives on the role of tension and the motion of the cylinders. There is an ongoing examination of the assumptions regarding friction and the trajectories of the cylinders, with some participants suggesting that the tension is related to the need for a force that balances their motion.

Contextual Notes

Participants note the presence of static friction, which complicates the analysis of the system's motion. There is also a mention of the rod being modeled as non-expandable, which influences the discussion about the trajectories of the cylinders.

  • #31
zemaitistrys said:
How would you define the quantity required to find in the problem then? Torsion sure ain't measured in Newtons.
No, it's a torque, in Newton metres.
 
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  • #32
haruspex said:
No, it's a torque, in Newton metres.

It was specified to find a force, the distinction is quite clear in the language the problem is written in.
 
  • #33
zemaitistrys said:
It was specified to find a force, the distinction is quite clear in the language the problem is written in.
Then I see no way to answer the question.

Edit: maybe I do...
The original post said, specifically, a tension. Let's ignore that, and also suppose the rod acts as a smooth axle for each cylinder, so cannot exert an axial torque. For simplicity, suppose it contacts each cylinder only at two bearings, one at each end of the cylinder.
There will be four forces on the rod from these bearings. Each is parallel to the plane and normal to the rod.
The combination of the two forces from one cylinder can be thought of as one force plus a torque normal to the plane. If we ignore the torque, we could consider this net force as the force the question is after.
 
Last edited:

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