# Energy

Energy is the capacity or the ability to do work. It can be categorized into two forms:

• Transient Energy (Mechanical Work, Heat)
• Stored Energy (Kinetic, Potential)

## Mechanical Work

The product of the displacement (distance traveled) of the body multiplied by the component of the force in the direction of the displacement.

$Work\quad =\quad Force\quad \times \quad Distance$

 Imperial SI Unit W = Work ft-lbf N-m or Joule F= Force applied lbf Newton (N) d = Distance traveled ft m

Example 1. Find the amount of Work being applied when a weight of 1000 lb is lifted through a distance of 124 inches and express it in imperial unit standard as ft-lbf.

W = F x d
W = 1000 x (124 in x (1ft/12in))
W = 1000 x 10.33
W = 10330 ft-lbf

Example 2. A ventilating fan having a mass of 165 kg is hoisted 96m from the ground to the roof of a building. Neglecting friction and other losses, compute the work done. Express the work in SI unit.

W =F x d = m x g x d

W = (165 kg) x (9.8 m/s^2) x (96 m)

W = 155,343 J

# Power

Power is the time rate at which work is done or work per unit time.
$Power\quad =\quad Work\quad /\quad Time$

 imperial SI P = Power ft-lbf /sec Watt (J/sec) W = Work ft-lbf N-m or Joule (J) T = Time sec sec

The horsepower (hp) is a widely used unit in the Imperial system

1 hp = 550 ft-lbf /sec = 746 watts

Example 1. Determine the power required in kilowatts and horsepower to move an elevator weighting 2000 lbf vertically through 40 ft in 10 seconds.

In Imperial

$P=\frac { W }{ T } =\frac { (F\times d) }{ T } =\frac { ({ 2000 }{ lb }_{ f }\quad \times \quad 40ft) }{ 10sec } =\quad 8000\quad ft-{ lb }_{ f }/sec$

In Horsepower

$P\quad =\quad \frac { 8000\quad ft-{ lb }_{ f } }{ sec } \div \frac { 500\quad ft-{ lb }_{ f } }{ sec } hp\quad =\quad 14.5\quad hp$

In Kilowatts

$P\quad =\quad 14.5\quad hp\quad \times \quad .746\frac { kW }{ hp } \quad =\quad 10.8\quad KW$