WORK, ENERGY AND POWER
Meaning of Work, Energy, and Power
a) Work
Definition: Work is said to be done when a force is applied on an object and the object moves in the direction of the force.
Conditions for Work to be Done:
- A force must be applied. If there is no force, there is no work.
- The object must move. If the object does not move, no work is done.
- The displacement of the object must have a component in the direction of the force applied.
Formula for Work:
W = F × d × cos θ
Where:
- W = Work done (in joules, J)
- F = Force applied (in newtons, N)
- d = Displacement of the object (in meters, m)
- θ = Angle between the force and displacement
Unit of Work: Joule (J)
1 Joule: The work done when a force of 1 N displaces an object by 1 m in the direction of the force.
b) Energy
Definition: Energy is the capacity to do work.
Forms of Energy:
Kinetic Energy (KE): Energy possessed by a body due to its motion.
Formula: KE = 1/2 × m × v²
Where: m = mass (kg), v = velocity (m/s)
Potential Energy (PE): Energy possessed by a body due to its position or configuration.
Formula: PE = m × g × h
Where: m = mass (kg), g = acceleration due to gravity (9.8 m/s²), h = height (m)
Unit of Energy: Joule (J)
c) Power
Definition: Power is the rate at which work is done or energy is transferred.
Formula for Power:
P = W / t
Where:
- P = Power (in watts, W)
- W = Work done (in joules, J)
- t = Time taken (in seconds, s)
Unit of Power: Watt (W)
1 Watt: The power of a device that does 1 joule of work in 1 second.
Relationship Between Work, Energy, and Power
- Work done on an object results in a change in energy.
- Energy is required to do work.
- Power indicates how fast work is done or energy is transferred.
- Energy can exist in different forms, such as potential or kinetic energy.
- The total energy of a system remains constant according to the law of conservation of energy.
Summary Table:
| Concept |
Formula |
Unit |
| Work (W) |
W = F × d × cos θ |
Joule (J) |
| Kinetic Energy (KE) |
KE = 1/2 × m × v² |
Joule (J) |
| Potential Energy (PE) |
PE = m × g × h |
Joule (J) |
| Power (P) |
P = W / t |
Watt (W) |
Calculations Involving Work, Energy, and Power
Work: Calculate the work done if a force of 20 N moves an object 5 m in the direction of the force.
W = F × d = 20 × 5 = 100 J
Kinetic Energy: Calculate the kinetic energy of a 2 kg ball moving at 3 m/s.
KE = 1/2 × m × v² = 1/2 × 2 × 3² = 9 J
Potential Energy: Find the potential energy of a 5 kg object lifted to a height of 4 m.
PE = m × g × h = 5 × 9.8 × 4 = 196 J
Power: A person does 200 J of work in 10 s. Calculate the power.
P = W / t = 200 / 10 = 20 W
Relationship Between Potential and Kinetic Energy
- Energy can change from one form to another.
- When a ball falls from a height, potential energy is converted into kinetic energy.
- Law of Conservation of Energy: Energy cannot be created or destroyed; it can only change from one form to another.
- Potential energy is stored energy due to position, while kinetic energy is the energy of motion.
- Energy transformation occurs in many everyday situations, such as in pendulums, roller coasters, and moving vehicles.
