Energy

Definition and Properties of Energy

Energy is defined as the ability of a system to do work or produce heat. It is a fundamental concept in physics, underlying all physical processes.

• Forms of Energy: Energy exists in various forms (mechanical, thermal, chemical, etc.).

• Transfer and Transformation: Energy can be transferred from one object to another and transformed from one form to another.

• Conservation: The total energy in a closed system remains constant (Law of Conservation of Energy).

Main Idea: Energy cannot be created or destroyed; it can only be transferred or transformed.

Work

Definition and Calculation of Work

Work is done when a force acts on an object and causes it to move in the direction of the force.

• Formula:

• W: work (in joules, J)

• F: force (in newtons, N)

• d: distance (in meters, m)

• If the object does not move, no work is done ().

• Doubling the force or the distance doubles the work done.

Example: Pushing against a stationary wall does no work on the wall ().

Power

Definition and Calculation of Power

Power measures how quickly work is done.

• Formula:

• P: power (in watts, W)

• W: work (in joules, J)

• t: time (in seconds, s)

Example: Two people climb the same stairs (same work), but the one who climbs faster uses more power.

Mechanical Energy

Forms of Mechanical Energy

Mechanical energy is the energy associated with the motion and position of an object. It has two main forms:

• Potential Energy (PE): Energy due to position.

• Kinetic Energy (KE): Energy due to motion.

Total Mechanical Energy:

Conservative vs. Non-Conservative Forces

Types of Forces and Their Effects on Mechanical Energy

• Conservative Forces: Do not change the total mechanical energy when acting alone.

  • Examples: Gravity, elastic (spring) force, electric force.

• Non-Conservative Forces: Can change the total mechanical energy (usually convert it to heat or other forms).

  • Examples: Friction, external pushes/pulls, normal forces, tension.

Potential Energy

Definition and Calculation of Potential Energy

Potential energy is stored energy due to an object's position or configuration.

• Examples: Raised object (gravitational PE), stretched rubber band or drawn bow (elastic PE).

• Gravitational Potential Energy:

• m: mass (kg)

• g: gravitational acceleration ( on Earth)

• h: height above reference point (m)

• Gravitational PE depends only on the change in vertical position, not the path taken.

Kinetic Energy

Definition and Calculation of Kinetic Energy

Kinetic energy is the energy of motion.

• Formula:

• m: mass (kg)

• v: velocity (m/s)

• Kinetic energy increases with the square of the speed. If speed doubles, kinetic energy increases by four times.

Memory Trick: Momentum depends linearly on speed (), while kinetic energy depends on the square of speed.

Work-Energy Theorem

Relationship Between Work and Kinetic Energy

• Main Rule: The net work done on an object equals its change in kinetic energy.

• If the object starts from rest:

• If speed doubles, kinetic energy becomes four times greater; thus, stopping distance under the same friction force becomes four times greater.

Conservation of Energy

Law of Conservation of Energy

• Statement: Energy cannot be created or destroyed; it can only change forms.

• Example: In a bow and arrow, potential energy (PE) is converted to kinetic energy (KE) and some thermal energy due to friction.

Example Calculation:

• Bow has 50 J of PE

• Arrow receives 40 J of KE

• Remaining 10 J becomes heat

Kinetic Energy vs. Momentum

Comparison Table

Summary Table: Key Concepts and Formulas