# Power

on . Posted in Classical Mechanics

Mechanical power, abbreviated as P, is the rate at which work is done or energy is transferred by a machine or system.  It is a measure of how quickly work can be done.

The mechanical power output of a machine or system can be calculated by multiplying the force applied by the object by its velocity, or by multiplying the torque applied by the object by its rotational speed.  In the case of an engine or motor, the mechanical power output is usually expressed in terms of horsepower, and represents the amount of power that can be used to perform useful work, such as propelling a vehicle or turning a machine.

Mechanical power is an important concept in physics and engineering, and is used to design and optimize various types of machines and systems, from engines and motors to turbines and generators.

## Power with displacement formula

$$\large{ P = \frac{F \; d}{t} }$$
Symbol English Metric
$$\large{ P }$$ = power $$\large{W}$$ $$\large{\frac{kg-m^2}{s^3}}$$
$$\large{ d }$$ = displacement $$\large{ft}$$ $$\large{m}$$
$$\large{ F }$$ = force $$\large{lbf}$$ $$\large{N}$$
$$\large{ t }$$ = time $$\large{sec}$$ $$\large{s}$$

## Power with Velocity formula

$$\large{ P = F \; v }$$
Symbol English Metric
$$\large{ P }$$ = power $$\large{W}$$ $$\large{\frac{kg-m^2}{s^3}}$$
$$\large{ F }$$ = force $$\large{lbf}$$ $$\large{N}$$
$$\large{ v }$$ = velocity $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$

## Power with Work formula

$$\large{ P = \frac{W}{t} }$$
Symbol English Metric
$$\large{ P }$$ = power $$\large{W}$$ $$\large{\frac{kg-m^2}{s^3}}$$
$$\large{ t }$$ = time $$\large{sec}$$ $$\large{s}$$
$$\large{ W }$$ = work $$\large{lbf-ft}$$ $$\large{J}$$

Tags: Power Equations