Work

Written by Jerry Ratzlaff on . Posted in Thermodynamics

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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 formulawork 1

\(\large{ W = F  d  }\)

\(\large{ W = F  d \; cos \;\theta }\)

Where:

\(\large{ d }\) = distance or displacement

\(\large{ F }\) = force

\(\large{ W }\) = work

\(\large{ \theta }\)  (Greek symbol theta) = the angle between the force vector F and the displacement vector d

Solve for:

\(\large{ F = \frac {W}{d} }\)

\(\large{ d = \frac {W}{F} }\)

Total Work

Total Work formula

\(\large{W_t = \frac {1}{2} m v_f^2   \;-\;   \frac {1}{2} m v_i^2   }\)

Where:

\(\large{v_f }\) = final velocity

\(\large{ v_i }\) = initial velocity

\(\large{m }\) = mass

\(\large{W_t }\) = total work

Rotational Work

Rotational Work formula

\(\large{ W_r = \tau \theta  }\)

Where:

\(\large{ W_r }\) = rotational work

\(\large{ \tau }\)  (Greek symbol tau) = rotational force

\(\large{ \theta }\)  (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

\(\large{ W=\Delta E = E_2 \;-\; E_1 }\)

Where:

\(\large{ E }\) = energy

\(\large{ \Delta E }\) = energy differential

\(\large{ W }\) = work

Work Power

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

Work Power Formula

\(\large{ P = \frac {W}{t} }\)

Where:

\(\large{P, P_w }\) = power

\(\large{ t }\) = time

\(\large{ W }\) = work

Solve for:

\(\large{ W = Pt }\)

\(\large{ t = \frac {W}{P} }\)

energy Power Efficiency

\(\large{ Efficency \%  = \frac {Usefull \; Energy} {Total \; Energy} \; \times \; 100 \% =  \frac {Usefull \; Power} {Total \; Power} \; \times \; 100 \%     }\)