Which one of the following is not a conservative force ?
Frictional force
Understanding Conservative and Non-Conservative Forces in Physics
Forces in physics can be broadly classified into two categories: conservative forces and non-conservative forces. This classification depends on how the force affects the mechanical energy of a system and how the work done by the force depends on the path taken.
What is a Conservative Force?
A conservative force is a force for which the work done in moving an object from one point to another depends only on the initial and final positions of the object, and not on the path taken between these points. Equivalently, the work done by a conservative force around any closed path is zero. Conservative forces are associated with potential energy. When a conservative force does positive work, the potential energy of the system decreases, and when it does negative work, the potential energy increases. Total mechanical energy (sum of kinetic and potential energy) is conserved in a system where only conservative forces do work.
Examples of conservative forces include:
- Gravitational force
- Electric force (for static charges)
- Elastic force (like the force exerted by an ideal spring)
What is a Non-Conservative Force?
A non-conservative force is a force for which the work done in moving an object from one point to another depends on the path taken. The work done by a non-conservative force around a closed path is generally non-zero. Non-conservative forces typically dissipate mechanical energy from a system, often converting it into other forms of energy like heat or sound. Mechanical energy is not conserved when non-conservative forces do work.
Examples of non-conservative forces include:
- Frictional force (sliding friction, rolling friction, fluid friction)
- Air resistance or drag force
- Tension in a rope (if it changes direction or magnitude unpredictably)
- Propulsion force (like from a motor)
Analyzing the Given Options
Let's examine each force listed in the options based on the definitions of conservative and non-conservative forces:
- Frictional force: Friction always opposes motion or impending motion. The work done by friction depends on the distance traveled along the path. For instance, pushing a box across a floor for a longer path between two points requires more work against friction than a shorter path. Also, friction typically generates heat, dissipating energy. Thus, frictional force is a non-conservative force.
- Electric force: The electric force between stationary charges is a central force and is associated with electric potential energy. The work done by the electric force in moving a charge between two points is independent of the path taken. Therefore, electric force is a conservative force.
- Gravitational force: The gravitational force is a conservative force. The work done by gravity in moving an object between two points depends only on the difference in height, regardless of the path (e.g., climbing a steep hill vs. a gentle slope to the same height). It is associated with gravitational potential energy.
- Spring force: The force exerted by an ideal spring ($\vec{F} = -k\vec{x}$) is also a conservative force. The work done by a spring in moving an object from one position to another depends only on the initial and final displacements from the equilibrium position, not the path taken. It is associated with elastic potential energy.
Based on this analysis, the frictional force is the only force among the options that is not a conservative force.
Revision Table: Types of Forces
| Force Type | Path Dependence of Work | Work Done in Closed Loop | Associated Potential Energy | Energy Conservation (if only this force acts) | Example |
|---|---|---|---|---|---|
| Conservative Force | Path Independent | Zero | Yes | Mechanical Energy is Conserved | Gravity, Electric Force, Spring Force |
| Non-Conservative Force | Path Dependent | Non-Zero (generally) | No (or not directly) | Mechanical Energy is Not Conserved (often dissipated) | Friction, Air Resistance |
Additional Information on Forces and Work-Energy Theorem
The distinction between conservative and non-conservative forces is important in understanding the work-energy theorem and the concept of energy conservation. The total work done on an object by all forces is equal to the change in its kinetic energy:
\(W_{total} = \Delta KE\)
If we separate the total work into work done by conservative forces (\(W_c\)) and work done by non-conservative forces (\(W_{nc}\)), we have:
\(W_c + W_{nc} = \Delta KE\)
For conservative forces, the work done is related to the change in potential energy (\(\Delta PE\)) by \(W_c = -\Delta PE\). Substituting this into the equation:
\(-\Delta PE + W_{nc} = \Delta KE\)
Rearranging this gives:
\(W_{nc} = \Delta KE + \Delta PE\)
\(W_{nc} = \Delta (KE + PE)\)
\(W_{nc} = \Delta E_{mechanical}\)
This equation shows that the work done by non-conservative forces equals the change in the total mechanical energy of the system. If only conservative forces do work (\(W_{nc} = 0\)), then \(\Delta E_{mechanical} = 0\), meaning the mechanical energy is conserved.
Understanding this difference helps predict how energy is transferred and transformed in physical systems.
Important Questions from Potential Energy
Which of the following is an example of gravitational potential energy?
What type of energy conversion takes place during the thunder of clouds?
The potential difference is 40V. Find the work done to transmit a charge of 0.5C?
Which of the following terms is used for stored energy that depends upon the relative position of various parts of a system?
A man picks up a bag of weight of 15 kg from the ground and puts it on his head 1.5 m above the ground. What is the work done by him on the bag? ( g = 10 m/s 2 )
