- #1
eurekameh
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I don't understand why the force is acting through a distance of 1.2pi, even though the center of the disk clearly moves a distance of 0.6pi.
Work-Energy: Force Acting Through 1.2pi Despite 0.6pi Move
- Thread starter eurekameh
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SUMMARY
The discussion centers on the relationship between force, distance, and energy in a system involving a disk and a cord. It is established that while the center of the disk moves a distance of 0.6π, the force acts through a distance of 1.2π due to the unwinding cord. The conversation emphasizes that the force not only contributes to translational kinetic energy but also generates a moment about the center of mass, which affects the rotational kinetic energy. Both translational and rotational kinetic energies are crucial in understanding the total work done in this scenario.
PREREQUISITES- Understanding of translational and rotational kinetic energy
- Familiarity with the concept of work and energy in physics
- Knowledge of moments and their effect on rotational motion
- Basic principles of circular motion and forces
- Study the principles of work-energy theorem in rotational dynamics
- Learn about the relationship between torque and angular displacement
- Explore the conservation of energy in systems involving both translational and rotational motion
- Investigate the effects of cord tension on the motion of connected bodies
Physics students, educators, and anyone interested in the mechanics of rotational systems and energy transfer in physical systems.
I don't understand why the force is acting through a distance of 1.2pi, even though the center of the disk clearly moves a distance of 0.6pi.
- #2
gneill
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The cord is unwinding. So the length of cord between where it meets the disk and whatever it is that's pulling on the cord will grow longer. Clearly whatever is applying the force to the free end of the cord has to mover further than the disk's center.
- #3
eurekameh
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Isn't the force also causing a moment about the center of mass? Shouldn't this contribute to the work done?
- #4
gneill
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eurekameh said:
Doing work results in a change in energy, in this case a change in the energy of motion. Can you identify where the energy of motion is going to end up in this case?
- #5
eurekameh
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Translational and rotational kinetic energy. The force moves through a distance of 1.2pi. But it is also causing a moment through an angle of 2pi. Shouldn't this moment through an angle also be contributing to the total kinetic energy (translational and rotational) of the disk?
- #6
gneill
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eurekameh said:
You've identified translational and rotational kinetic energies to be where the work energy ends up. That's good. The solution included with the question deals with both.