Jamming a Pulley: Assessing Stress on Shaft & Hole

AI Thread Summary
Jamming a pulley by inserting an object creates normal stresses at the hole and torsional stress on the shaft due to the motor's torque. The magnitude of these stresses is influenced by factors such as the shaft's radius, the distance of the holes from the pulley center, and the shaft's length. The moment of inertia plays a crucial role, with the highest torsional stress occurring in the object with the largest moment of inertia. Additionally, the normal stress on the hole increases when the applied force is closer to the pulley center due to a smaller radius. Understanding these stress distributions is essential for assessing the mechanical integrity of the system.
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A pulley-and-shaft is connected to a motor which applies torque to spin the pulley as shown below:
image392.jpg

Now imagine someone jams machine by sticking a broom into one of the holes of the pulley.
I would imagine there would be normal stresses at the hole (location of jam) and torsional stress on the shaft (from the motor attempting to continue turning), but magnitudes of these stresses would depend on factors like radius of the shaft, distance of holes from the center of the pulley, length of shaft, etc.

Are my assumptions reasonable?
 

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In order to jam the pulley, you need to apply a torsional stress on the pulley. In this case, you apply normal stress on the holes (which is torsional on the pulley) and torsional on the shaft, I agree.

I suppose the moment of inertia (of pulley and shaft) is the key in this case. The biggest torsional stress will be applied in the object with the biggest moment of inertia.
The moment of inertia depends on distribution of mass, the total mass, the geometry and the dimensions of the object.

The normal stress that is applied on the specific hole (in which you stick the broom) depends on the distance from the center of the pulley. When you apply this stress near the center, it must be bigger, because radius is smaller there.
 
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