Why is work done by a nonconservative force negative

In summary, the conversation discusses the concept of work done by a nonconservative force and its relationship to potential energy. The speaker questions why the work done on a test charge is negative when trying to push it towards a negative charge, and explains that this is because the force exerted is in the opposite direction of the charge's movement. The conversation also touches on the idea that non-conservative forces do not have potential energy associated with them, and that the work done by a non-conservative force is determined by its own formula.
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In my textbook it says that work done by a nonconservative force (an applied force) has the same sign as the change of potential energy?

For instance, if I push a positive test charge from an infinite distance away to a negative charge, then the test charge goes from high potential energy to low potential energy. Why is the work that I am doing on it negative? Shouldn't the work I'm doing on it be positive, because I'm losing energy trying to push the test charge?
 
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  • #2
You are not pushing the positive charge toward the negative charge. You are trying to hold it back. So the force you are exerting is in the opposite direction from the direction that the charge is moving.

Chet
 
  • #3
Are you sure this is the exact formulation in your book?
A non-conservative force does not have a potential energy associated with it. So in general you can have a non-conservative force and no potential energy to speak of. Why would the work of this non-conservative be the negative of a non-existent potential energy?

If you have both conservative and non-conservative forces, the work of the conservative force is (by definition) the negative of the change in PE associated with this conservative force. The work of the non-conservative is whatever the formula for work provides, for that force.
 

1. Why is work done by a nonconservative force negative?

The work done by a nonconservative force is negative because the force does not follow the principle of conservation of energy. This means that the energy of the system is not constant and can be lost or gained. In other words, the nonconservative force causes a change in the total energy of the system, resulting in a negative work value.

2. What is a nonconservative force?

A nonconservative force is a type of force that does not follow the principle of conservation of energy. These forces are usually friction, air resistance, or any force that causes energy to be lost or gained in a system. Nonconservative forces are often called dissipative forces because they cause energy to dissipate or be lost as heat.

3. How is work calculated for a nonconservative force?

The work done by a nonconservative force can be calculated using the equation W = ∆K + ∆U, where W is the work done, ∆K is the change in kinetic energy, and ∆U is the change in potential energy. Since nonconservative forces cause a change in the total energy of the system, both ∆K and ∆U will have a negative value, resulting in a negative work value.

4. What is the difference between a conservative and nonconservative force?

The main difference between a conservative and nonconservative force is that conservative forces follow the principle of conservation of energy, while nonconservative forces do not. This means that conservative forces do not cause a change in the total energy of the system, while nonconservative forces do. Examples of conservative forces include gravity and spring forces, while examples of nonconservative forces include friction and air resistance.

5. Why is the concept of nonconservative forces important?

The concept of nonconservative forces is important because it helps us understand the behavior of energy in a system. By understanding how nonconservative forces affect the total energy of a system, we can better predict the motion and behavior of objects in real-life situations. This concept also has practical applications in fields such as engineering, physics, and mechanics.

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