Rate Of Doing Work

Key Notes:

Definition of Work:

• Work is done when a force is applied to an object, and the object moves in the direction of the force.
• Formula: W = F × d × cos⁡ θ where:
  • W is work,
  • F is force,
  • d is displacement,
  • θ is the angle between force and displacement.

Rate of Doing Work:

• The rate at which work is done is called power.
• Power measures how quickly or slowly work is performed.

Definition of Power:

• Power is defined as the amount of work done per unit time.
• Formula: P = W/t
  • P is power,
  • W is work done,
  • t is the time taken.

Unit of Power:

• The SI unit of power is the watt (W).
• 1 watt = 1 joule / second (J/s)

Larger Units of Power:

• Kilowatt (kW): 1 kW = 1000 W.
• Horsepower (hp): 1 hp ≈ 746 W.

Energy and Power:

• Power is closely related to energy transfer.

Energy transferred = Power × Time

Practical Examples:

• A person climbing stairs at different speeds demonstrates different rates of doing work.
• Electrical appliances like bulbs and motors have power ratings that indicate the energy they consume per unit time.

Relation to Efficiency:

• Power and work are used to calculate the efficiency of machines, which is given by:

Graphical Representation:

• Work versus time graphs can help visualize power, as the slope of the graph gives the power.

Factors Affecting Power:

• The amount of work done.
• The time taken to do the work.

Let’s practice!