# Work, Power, and Energy

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Work

Work is the overcoming of resistance through space and is the measure of force x distance. Since the unit of force is a pound and the unit of distance is a foot, the product of a foot by a pound is a unit of work. This is expressed in ''foot pounds'' or ''Newton meters'."

Energy is the capacity of doing work and comes in many forms such as kinetic energy (KE) and potential energy (PE)

Work, power, and energy are scalar quantity having direction, some of these include area, density, entropy, length, mass, pressure, speed, temperature, and volume.

### Work formula

$$W = F d$$

$$W = F d cos \theta$$

Where:

$$W$$ = work

$$F$$ = force

$$d$$ = distance or displacement

$$\theta$$ = the angle between the force vector F and the displacement vector d

Solve for:

$$F = \frac {W}{d}$$

$$d = \frac {W}{F}$$

## Total Work

### Total Work formula

$$W_t = \frac {1}{2} m v_f^2 \;-\; \frac {1}{2} m v_i^2$$

Where:

$$W_t$$ = total work

$$m$$ = mass

$$v_i$$ = initial velocity

$$v_f$$ = final velocity

## Rotational Work

### Rotational Work formula

$$W_r = \tau \theta$$

Where:

$$W_r$$ = rotational work

$$\tau$$ (Greek symbol tau) = rotational force

$$\theta$$ (Greek symbol theta) = angular position

## Work Energy

Energy is the capacity of doing work.  Energy is never created or destroyed but external work performed on a conservative system goes into changing the system's total energy.

### Work Energy formula

$$W=\Delta E = E_2 \;-\; E_1 \;$$

Where:

$$W$$ = work

$$\Delta E$$ = energy differential

$$E$$ = energy

## Work Power

Power ( $$PWR$$ ) is the rate of doing work or the rate of using energy per unit time.

### Work Power Formula

$$P = \frac {W}{t}$$

Where:

$$P$$ or $$P_w$$ = power

$$W$$ = work

$$t$$ = time

Solve for:

$$W = Pt$$

$$t = \frac {W}{P}$$

## energy Power Efficiency

$$Efficency \% = \frac {Usefull \; Energy} {Total \; Energy} \; \times \; 100 \% = \frac {Usefull \; Power} {Total \; Power} \; \times \; 100 \%$$