# Mechanical power, definition, equation, examples, and more.

** **In physics, power is a concept, where the rate of doing work in unit time is called power. Further, it may be said that the amount of energy converted or transferred per unit of **time is called power. **Then what is mechanical power? It is the power of the machine and the movement of the different components such as the drivetrain of a vehicle.

**Mechanical power definition;**

** **In physics, power is a concept, where the rate of doing work in unit time is called power. Further, it may be said the **amount of energy converted or transferred per unit of time is called power. **Then what is mechanical power? It is the power of the machine and the movement of the different components such as the drivetrain of a vehicle. Mechanical power is associated with the moving components of a machine or a mechanical system.

The machine may be driven by electricity, steam, gas, or any combustion of fuel, etc. **It is power output means how fast the engine can start working, after receiving the power from fuel.** However, the power input is different, where **how fast the energy of the fuel is converted to power to use for the vehicle.**

SI unit of power is applied to any power including mechanical power. Thus,

- In the SI system, a unit of power is the watt(w), which is Joules per second (J/S).
- SI base units-kg.m
^{2}.s^{-3} - Dimensional formula-M
^{1}L^{2}T^{-3}

Physically the mechanical power of a moving object is defined by the amount of energy or work W is converted or transferred within a specific time. Hence

- Power is expressed as=
**P= w/t,**where P is power, w is work, and time is t. - or the amount of change in energy divided by the change in time
**, P= ΔE/ Δt**

Sometimes the power of motor vehicles and machines is expressed in the term horsepower (hp). One horsepower is approximately 745.7 watts.

**Power in linear motion:**

When any force is applied to an object in linear motion, the object moves either forward or backward along a straight line. In such a situation power can be expressed by a simple formula taking force, distance, and velocity into account. Now work W can be defined as force F multiplied by distance d.

**Equation of power;**

Now equation of power can be;

**P=Fd/t**

In linear motion, velocity (v )is calculated by dividing distance by time. Now power can be expressed as;

**P=Fd/t=Fv**

**Power in Rotational motion;**

Power in rotational motion is as important as power in linear motion. Here power is delivered to a system, that is rotating a fixed axis. In such cases, power is the product of a force on an object and the product of torque on a shaft, and the angular velocity of the shaft.

In variable force over a three-dimensional curve C, then the work is expressed in terms of the **line integral,**

**W=ʃ _{c} F.dr=ʃ_{Δt} F.dr/dt dt=ʃ**

_{Δt}F

**From the fundamental theorem of calculus (integration), It is clear that **

**P=dw/dt=d/dt(F.S)=F.ds/dt=F.v.**

**P=Fv**

Hence the above formula is valid for any situation.

It is further to note that higher force F can only be achieved with a correspondingly lower speed V.

**F=P/V**

Further more work done within a specific period means more power is consumed. However, if mechanical power is from a heat engine like a power plant, it is limited by the **second law of thermodynamics****.**

**Examples of mechanical power.**

Some examples are;

- The engine of a motor car.
- The engine of a train.
- The engine of an aircraft.
- Pulleys inside an antique clock.

**Conclusion;**

Mechanical power is referred to as time derivatives of work and is associated with machines and the movement of their different components. Normally it is a combination of force and movement. More power consumed means more work is done.

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[…] Mechanical power is a type of power defined as the rate at which work is done or energy is transferred by a machine or a mechanical system. It is usually measured in watts (W) or horsepower (hp) and is calculated by multiplying the force applied by a machine with the distance over which the force is applied per unit time. In other words, mechanical power is the amount of work done per unit time. It is a key concept in the field of engineering and is used to quantify the performance of various mechanical systems such as engines, motors, and turbines. […]