Question

Which of the following is a conservative force? (A) Air resistance (B) Friction (C) Gravity (D) Convection

Short answer

C) Gravity

Step-by-step solution

Understand the Concept of Conservative Force

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. Additionally, the work done by or against a conservative force in moving a particle through a closed loop is zero.

Identify Non-Conservative Forces

Common examples of non-conservative forces include friction and air resistance. These forces dissipate energy as heat, making the work done path-dependent and non-recoverable.

Evaluate Each Option

Let's evaluate each force:- Air resistance: This is a non-conservative force as the work done against it depends on the path.- Friction: This is also a non-conservative force as it dissipates energy as heat.- Gravity: This is a conservative force because the work done by gravity depends only on the initial and final positions, not the path taken.- Convection: This is a process, not a force, and it typically involves non-conservative forces since it relates to the movement of heat.

Identify the Conservative Force

Based on the evaluations, gravity is the only conservative force among the given options.

Key concepts

Gravity

Gravity is a conservative force. This means that the work done by gravity on an object only depends on the initial and final positions of the object, not the path taken. For instance, if you lift a book and then place it back on the same spot, the work done by gravity is zero, since it forms a closed loop. Gravity always acts downwards, towards the center of the Earth.
Key points to remember about gravity include:

• It depends only on the vertical displacement of an object.
• It can store energy in the form of gravitational potential energy, calculated by the formula: \( U = mgh \), where \( U \) is potential energy, \( m \) is mass, \( g \) is the acceleration due to gravity, and \( h \) is height.
• Since it is a conservative force, energy involved in gravity can be fully recovered if the process is reversed.

Friction

Friction is a non-conservative force. It opposes the relative motion between two surfaces in contact. Unlike conservative forces, the work done by friction depends on the path taken. This force converts kinetic energy into heat, which is why you often feel warmth when you rub your hands together.
Main points about friction include:

• It always acts in the direction opposite to motion.
• It leads to the loss of mechanical energy as heat.
• The work done by friction can never be recovered entirely, making it path-dependent.

When analyzing problems involving friction, keep in mind that it is crucial for tasks like walking and driving, but also contributes to wear and tear over time.

Air Resistance

Air resistance, also known as drag, is another non-conservative force. It acts opposite to the direction of an object moving through the air, causing a loss in kinetic energy.
Key characteristics of air resistance include:

• It depends on factors like the speed of the object, the density of the air, the cross-sectional area of the object, and the drag coefficient.
• It results in energy dissipation, often observed as the object slowing down unless additional force is applied.
• The work done against air resistance is path-dependent and non-recoverable, dissipating energy as heat.

Air resistance becomes more noticeable at higher speeds, and it is why streamlined designs are used in vehicles and aircraft to minimize its impact.

Work-Energy Principle

The work-energy principle is a cornerstone of classical mechanics. It states that the work done by all forces acting on an object is equal to the change in its kinetic energy.
This principle is formulated as:

• \( W_{total} = \triangle K \), where \( W_{total} \) is the total work done, and \( \triangle K \) is the change in kinetic energy.
• For conservative forces, the work done can convert between kinetic and potential energy, ensuring total mechanical energy is conserved in a closed system.
• For non-conservative forces like friction and air resistance, some of the mechanical energy is transformed into other forms of energy such as heat, making it less straightforward to track.

Understanding how to apply the work-energy principle helps in solving various physics problems, from simple motion to complex systems.