Work-Energy: Force Acting Through 1.2pi Despite 0.6pi Move

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In summary, the force acting through a distance of 1.2pi and causing a moment around the center of mass is contributing to the translational and rotational kinetic energies of the disk. The length of cord between the disk and the force is also increasing as the cord unwinds, resulting in a change in energy of motion.
  • #1
eurekameh
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2ls6ziu.png

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.
 
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  • #2
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
Isn't the force also causing a moment about the center of mass? Shouldn't this contribute to the work done?
 
  • #4
eurekameh said:
Isn't the force also causing a moment about the center of mass? Shouldn't this contribute to the work done?

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
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
eurekameh said:
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?

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.
 

1. What is the relationship between work, energy, and force?

The work done on an object is equal to the change in its energy, and this change in energy is caused by a force acting on the object. In other words, work is the transfer of energy by a force.

2. How is work calculated in a scenario where a force acts through a distance of 1.2pi despite the object moving only 0.6pi?

In this scenario, the work done is calculated by multiplying the force by the distance through which it acts. So, the work done would be equal to 0.6pi times the force.

3. Can work be negative?

Yes, work can be negative. This happens when the force and the displacement of the object are in opposite directions. In this case, the work done is considered to be negative, which means that energy is being transferred away from the object.

4. How does energy change in the scenario described above?

In this scenario, the energy of the object does not change, as only half of the force is acting through the distance. Therefore, the object does not experience a change in energy.

5. Is it possible to have a non-zero force acting on an object, but no work being done?

Yes, it is possible. This can happen when the force is perpendicular to the displacement of the object. In this case, the force is not doing any work on the object, as the displacement is not in the same direction as the force.

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