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# Difference between Force and Power

**Force** and **Power** are two important concepts in physics. They might appear similar at first
sight, but they are completely different from each other. The most fundamental difference
between force and power is that Force is a cause that can change or try to change the state of
an object from rest to motion or motion to rest, whereas Power is the term used to express the
rate of doing work. Read this article to learn how Force is different from Power.

## What is Force?

**Force** is an external agent that can change the state of an object either from rest to motion or
from motion to rest. Sometimes, force is also said to be a push or pull on an object that
changes or tries to change the state or velocity of the object.

Force is generally denoted by the symbol "F". Force is a physical quantity which has both
magnitude and direction. Therefore, it is a vector quantity (quantity that have magnitude as
well as direction is referred to as a vector quantity). The SI unit of force is **Newton**, denoted
by N. Newton as the unit force is chosen in the honor of Sir Isaac Newton.

Mathematically, force is given by the Newton’s second law of motion, which is,

$$F\, =\, ma$$

Where, F is force in newton, m is mass of the object (in kg), and a is the acceleration in the object due to applied force measured in meter per square second. Therefore, the base unit of force is,

$$\mathrm{Unit\: of\: force\, =\,kg\, m\, s^{-2} }$$

Also,

$$\mathrm{1\: kg\, m\, s^{-2}\, =\,1\: Newton }$$

We can defined force of 1 N as under −

"When a force applied on an object of mass 1 kg accelerates it by 1 m/s^{2}, then the force is
said to be of 1 Newton."

There are two types of forces namely, **contact forces** and **non-contact forces**. A contact
force is one which can only act while two bodies are physically touching each other.
Whereas, non-contact force is the type of force that can act without any physical contact of
objects. Examples of contact forces include tension force, frictional force, air drag force,
spring force, etc. while the gravitational force, electrostatic force, magnetic force are
examples of non-contact forces.

## What is Power?

**Power** is defined as the rate of doing work. In other words, the rate at which work is done is
known as power. In more simple words, the work done per unit time is called power. Power
is usually represented by the symbol “P”. The SI unit of power is **Watt**, denoted by W. It is
taken in the honor of James Watt.

Mathematically, power is defined as defined as the ratio of work done and time, i.e.

$$\mathrm{Power,\mathit{P}\, =\, \frac{Workdone (W)}{Time\left ( \mathit{t} \right )}}$$

Here, work done (W) is measured in Joules (J), time (t) is measured in seconds (s). Hence, the unit of power is Joules per second (J/s).

Where,

$$\mathrm{1 Joule/sec \, = \, 1 Watt}$$

Sometimes, power is also measured in Horse Power (HP).

$$\mathrm{1\, HP \, =\, 745.7\, Watts}$$

In engineering and physics, power is one of the important physical quantities as it is used to express rating of all practical device and machine. For example, rating of an electric motor is expressed in terms of power developed by the motor such as 1 HP motor, 3 HP motor, and electric heater of 1000 Watts and so on.

After getting insights about description of force and power. Now, let us discuss the important differences between them.

## Differences between Force and Power

The following table highlights all the major differences between force and power −

Key |
Force |
Power |
---|---|---|

Definition |
An external agent that is capable of changing the state of a body either from rest to motion or motion to rest is called as force. |
The rate at which work is done in a system is known as power. |

Symbolic Representation |
Force is represented by the symbol "F". |
Power is represented by the symbol "P". |

Formula |
Force is given by the following formula, $$F\, =\, ma$$ Where, m is mass of body on which force is acting, and a is acceleration produced in the body due to action of force. |
Power is given by the following expression, $$\mathrm{\mathit{P}\, =\, \frac{W}{\left ( \mathit{t} \right )}}$$ Where, W is the work done, and t is the time in which work is complement. |

SI Unit |
The SI unit of force is Newton, denoted by N. |
The SI unit of power is Watt, denoted by W. |

Base Unit |
The base unit of force is
kilogram meter per square
second (kg m s |
The base unit of power is Joules per second (J/s). Where, 1 J/s is equal to 1 Watt. |

Relation of Force/Power with work |
Force applied on a body and it moves the body to a certain distance, then force is said to do work on the body. |
Power specifies rate at which work is done on a body. |

Types |
Force is divided into two types namely, contact force and noncontact force. |
Power is divided into two types namely mechanical power and electrical power. |

Examples |
Examples of forces are frictional force, gravitational force, electrostatic force, magnetic force, etc. |
Examples of powers are hydraulic power, wind power, active power, reactive power, etc. |

Real World Applications |
Force is used to drive a car, rotate the steering wheel, pull or push an object, stop a moving object, and many more. |
Power is used to determine rate of doing work to execute different types of analysis such as determining time to complete a task, energy required for work done, and so on. |

## Conclusion

From the above discussion, it is clear that force and power are two absolutely different physical quantities having different meaning and significant in nature and other physical processes. By analyzing above comparison, we could state the most significant difference between force and power which is, force is an agent that change the state of a body such as from rest to motion or motion to rest, whereas power is a measure of work done per unit time.