Points to Remember:
- Conservative forces and their relationship with potential energy.
- Work-energy theorem.
- Definition of positive work.
Introduction:
This question tests the understanding of the relationship between conservative forces and potential energy. A conservative force is a force with the property that the work done in moving a particle between two points is independent of the taken path. Examples include gravitational force and electrostatic force. The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. However, for conservative forces, this work is also related to the change in potential energy. Specifically, the work done by a conservative force is equal to the negative change in potential energy: W = -Î?PE.
Body:
1. Understanding Positive Work:
Positive work is done when the force and displacement are in the same direction. Imagine lifting a book. The gravitational force (a conservative force) acts downwards, but you apply an upward force to lift the book. Your applied force does positive work on the book. However, the gravitational force itself does negative work.
2. The Relationship between Conservative Forces and Potential Energy:
As mentioned earlier, the work done by a conservative force is equal to the negative change in potential energy (W = -Î?PE). If the conservative force does positive work (W > 0), then -Î?PE > 0, which implies that Î?PE < 0. This means the potential energy decreases.
3. Illustrative Example:
Consider a ball falling under gravity. Gravity is a conservative force. As the ball falls, gravity does positive work on it (force and displacement are in the same direction). Consequently, the ball’s potential energy decreases, and its kinetic energy increases.
4. Why other options are incorrect:
- (A) Increases: This is incorrect because positive work by a conservative force leads to a decrease in potential energy.
- (C) Remains unaltered: This is incorrect because doing work inherently changes the energy of the system.
- (D) Fluctuates: While potential energy can fluctuate in general, in the specific case of a conservative force doing positive work, it consistently decreases.
Conclusion:
When a conservative force does positive work on a body, its potential energy decreases. This is a direct consequence of the definition of conservative forces and the work-energy theorem. Understanding this relationship is crucial in various fields of physics, from mechanics to electromagnetism. The correct answer is (B). A thorough grasp of energy conservation principles is essential for solving problems involving forces and motion, promoting a deeper understanding of the physical world and its underlying laws.
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