when conservative force does positive work then why does potential energy of the system decreases

When we talk about conservative forces, we're usually referring to forces like gravity or spring forces that have a specific relationship with potential energy. To understand why the potential energy of a system decreases when a conservative force does positive work, let’s break it down step by step.

The Concept of Work and Energy

Work is defined as the transfer of energy that occurs when a force is applied over a distance. In the context of conservative forces, when positive work is done, it means that the force is acting in the direction of the displacement of the object. This typically results in an increase in kinetic energy or a change in the system's configuration.

Understanding Potential Energy

Potential energy is the stored energy in a system due to its position or configuration. For example, when you lift an object against the force of gravity, you are increasing its gravitational potential energy. Conversely, when the object falls, gravity does positive work on it, and its potential energy decreases.

Relationship Between Work and Potential Energy

The key principle here is that in a conservative force field, the work done by the force is equal to the negative change in potential energy. This can be expressed mathematically as:

• W = -ΔU

Where W is the work done by the conservative force and ΔU is the change in potential energy. If the work done is positive (W > 0), it implies that the potential energy (U) of the system must decrease (ΔU < 0).

Illustrative Example

Consider a ball being thrown upwards. As the ball rises, the force of gravity does negative work on it (since gravity acts downward while the ball moves upward). The energy transferred to the ball increases its kinetic energy, but at the same time, its gravitational potential energy increases. When the ball reaches its highest point and starts to fall, gravity does positive work on the ball, converting potential energy back into kinetic energy. Here, the potential energy decreases as the ball descends, illustrating the relationship between work and potential energy.

Why This Matters

This relationship is crucial in understanding energy conservation in physical systems. The total mechanical energy (kinetic + potential) remains constant in the absence of non-conservative forces (like friction). Therefore, when a conservative force does positive work, it effectively converts potential energy into kinetic energy or other forms of energy, leading to a decrease in potential energy.

Final Thoughts

In summary, when a conservative force does positive work, it indicates that energy is being transferred in a way that reduces the potential energy of the system. This interplay between work and potential energy is fundamental in physics, helping us understand how energy is conserved and transformed in various scenarios.