True or False. When non-conservative forces are present, the amount of work done increases with the length of the path.
This is in fact true.
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False. When non-conservative forces are present, the amount of work done is independent of the path taken. The work done by non-conservative forces depends only on the initial and final positions of the object, and not on the path taken between the two points.
True. When non-conservative forces are present, the amount of work done typically increases with the length of the path.
To understand this, let's first differentiate between conservative and non-conservative forces. Conservative forces, such as gravity and the spring force, depend only on the initial and final positions of an object, not on the path taken between them. Non-conservative forces, on the other hand, depend on the actual path taken and can vary depending on factors like friction, air resistance, or applied forces.
Now, let's consider the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. When only conservative forces are acting on an object, the work done can be determined simply by considering the initial and final positions. In this case, the path taken doesn't affect the work done.
However, when non-conservative forces are present, the total work done on an object can indeed vary with the path taken. This is because non-conservative forces, such as friction or air resistance, can dissipate energy as heat or other forms of energy. As a result, the work done by these forces is greater when the path is longer since there are more opportunities for energy dissipation along the way.
In conclusion, when non-conservative forces are present, the amount of work done increases with the length of the path due to the additional energy dissipated by these forces.